Annals of Physics, ISSN 0003-4916, 02/2008, Volume 323, Issue 2, pp. 500 - 526

We show that the technique of integration within normal ordering of operators [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480–494...

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Similarity transform and Weyl ordering covariance | Weyl ordering | Weyl ordered Wigner operator | Entangled state representation | Wigner transform | The integration for ket–bra operators | The IWWOP technique | The integration for ket-bra operators | the integration for ket-bra operators | PHASE-SPACE | PHYSICS, MULTIDISCIPLINARY | FRACTIONAL FOURIER-TRANSFORM | WIGNER-DISTRIBUTION | MODE | the IWWOP technique | entangled state representation | VIRTUE | IWOP TECHNIQUE | SQUEEZED STATES | similarity transform and Weyl ordering covariance | OPTICS | COHERENT-STATE REPRESENTATION | SYMPLECTIC TRANSFORMATIONS | Integrated approach | Mathematics | Statistical analysis | Physics | Quantum theory | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS | SIGNALS | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | TRANSFORMATIONS

Journal Article

Applied Optics, ISSN 1559-128X, 09/2016, Volume 55, Issue 26, pp. 7412 - 7421

We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval...

CONVERGENCE | IMAGE | ALGORITHMS | OPTICS | PROJECTIONS | RECONSTRUCTION | Projectors | Operators | Proximity | Algorithms | Mathematical analysis | Phase retrieval | Mathematical models | Gaussian | Physics - Instrumentation and Methods for Astrophysics

CONVERGENCE | IMAGE | ALGORITHMS | OPTICS | PROJECTIONS | RECONSTRUCTION | Projectors | Operators | Proximity | Algorithms | Mathematical analysis | Phase retrieval | Mathematical models | Gaussian | Physics - Instrumentation and Methods for Astrophysics

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 09/2016, Volume 289, Issue 13, pp. 1680 - 1691

We introduce a notion of (S+N)‐triangular operators in the Hilbert space using some basic ideas from triangular representation theory...

Maximal chain of orthogonal projections | 47A15 | 47A46 | invariant subspace | 47A45 | spectral operator | triangular representation | MATHEMATICS | GROWTH-CONDITIONS

Maximal chain of orthogonal projections | 47A15 | 47A46 | invariant subspace | 47A45 | spectral operator | triangular representation | MATHEMATICS | GROWTH-CONDITIONS

Journal Article

4.
Full Text
A new system of variational inclusions with ( H, η)-monotone operators in hilbert spaces

Computers and Mathematics with Applications, ISSN 0898-1221, 2005, Volume 49, Issue 2, pp. 365 - 374

...)-monotone operators in Hilbert space. Using the resolvent operator associated with ( H, η)-monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions...

Iterative algorithm | System of variational inclusion | Resolvent operator technique | ( H, η)-monotone operator | (H, η)-monotone operator | (H,eta)-monotone operator | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INEQUALITIES | resolvent operator technique | MANN | system of variational inclusion | PERTURBED ITERATIVE ALGORITHMS | MAPPINGS | iterative algorithm | PROJECTION METHODS | Operators | Algorithms | Approximation | Uniqueness | Hilbert space | Mathematical models | Inclusions | Convergence

Iterative algorithm | System of variational inclusion | Resolvent operator technique | ( H, η)-monotone operator | (H, η)-monotone operator | (H,eta)-monotone operator | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INEQUALITIES | resolvent operator technique | MANN | system of variational inclusion | PERTURBED ITERATIVE ALGORITHMS | MAPPINGS | iterative algorithm | PROJECTION METHODS | Operators | Algorithms | Approximation | Uniqueness | Hilbert space | Mathematical models | Inclusions | Convergence

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2020, Volume 362, p. 106958

We consider a positive and power-bounded linear operator T on Lp over a finite measure space and prove that, if TLp⊆Lq for some q...

Essential spectral radius | Quasi-compactness of positive operators | Uniform p-integrability | Ultrapower techniques | Convergence of semigroups | Geometry of Banach spaces | MATHEMATICS | SEMIGROUPS | PERIPHERAL SPECTRUM | CONTRACTIVE PROJECTIONS

Essential spectral radius | Quasi-compactness of positive operators | Uniform p-integrability | Ultrapower techniques | Convergence of semigroups | Geometry of Banach spaces | MATHEMATICS | SEMIGROUPS | PERIPHERAL SPECTRUM | CONTRACTIVE PROJECTIONS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2019, Volume 371, Issue 5, pp. 3721 - 3742

A scalar sequence \xi is said to be admissible for a positive operator A if A= \sum \xi _jP_j for some rank-one projections P_j, or, equivalently, if diag...

DIAGONALS | MATHEMATICS | PYTHAGOREAN THEOREM | FRAMES | MAJORIZATION | Schur-Horn theorem | diagonals of positive operators | Sums of projections | Kadison's carpenter theorem | PROJECTIONS | SUMS

DIAGONALS | MATHEMATICS | PYTHAGOREAN THEOREM | FRAMES | MAJORIZATION | Schur-Horn theorem | diagonals of positive operators | Sums of projections | Kadison's carpenter theorem | PROJECTIONS | SUMS

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2019, Volume 291, Issue 1, pp. 591 - 607

...–Toeplitz operator $$T_{\psi }$$ T ψ with symbol $$\psi =K^{-\alpha }$$ ψ = K - α maps from $$L^{p}$$ L p to $$L^{q}$$ L q continuously...

Pseudoconvex domain of finite type | 32A36 | Berman projection | Schur’s test | Mathematics, general | Mathematics | Primary 47B35 | Secondary 32A25 | Bergman kernel | Bergman–Toeplitz operator | 32T25 | MATHEMATICS | KERNEL | Bergman-Toeplitz operator | Schur's test | DIFFERENTIABILITY

Pseudoconvex domain of finite type | 32A36 | Berman projection | Schur’s test | Mathematics, general | Mathematics | Primary 47B35 | Secondary 32A25 | Bergman kernel | Bergman–Toeplitz operator | 32T25 | MATHEMATICS | KERNEL | Bergman-Toeplitz operator | Schur's test | DIFFERENTIABILITY

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2018, Volume 64, Issue 2, pp. 1092 - 1104

.... In this paper, we overcome this limitation by deriving new closed-form expressions for the proximity operator of such two-variable functions...

Closed-form solutions | proximal algorithms | Convex optimization | Rate-distortion | Estimation | epigraphical projection | Minimization | Convex functions | proximity operator | divergences | Optimization | Divergences | Epigraphical projection | Proximal algorithms | Proximity operator | MAXIMUM-LIKELIHOOD | COMPOSITE MONOTONE INCLUSIONS | DISTANCE MEASURES | IMAGE-RECONSTRUCTION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | FORMULATION | CHANNEL CAPACITY | F-DIVERGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MINIMIZATION | MASS-TRANSFER | Usage | Graph theory | Mathematical optimization | Estimation theory | Computational geometry | Operators | Proximity | Mathematical analysis | Optimization techniques | Data base management systems | Selectivity | Convexity | Convex analysis | Information Theory | Computer Science

Closed-form solutions | proximal algorithms | Convex optimization | Rate-distortion | Estimation | epigraphical projection | Minimization | Convex functions | proximity operator | divergences | Optimization | Divergences | Epigraphical projection | Proximal algorithms | Proximity operator | MAXIMUM-LIKELIHOOD | COMPOSITE MONOTONE INCLUSIONS | DISTANCE MEASURES | IMAGE-RECONSTRUCTION | ALGORITHM | COMPUTER SCIENCE, INFORMATION SYSTEMS | FORMULATION | CHANNEL CAPACITY | F-DIVERGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | MINIMIZATION | MASS-TRANSFER | Usage | Graph theory | Mathematical optimization | Estimation theory | Computational geometry | Operators | Proximity | Mathematical analysis | Optimization techniques | Data base management systems | Selectivity | Convexity | Convex analysis | Information Theory | Computer Science

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 11/2019, Volume 67, Issue 11, pp. 2173 - 2190

Let be a Hilbert space, the algebra of bounded linear operators on and a positive operator...

oblique projections | Shorted operators | minus order | MATHEMATICS | STAR | AXB | GENERALIZED INVERSES | RANGE | Operators (mathematics) | Hilbert space | Mathematical analysis | Linear operators | Infimum

oblique projections | Shorted operators | minus order | MATHEMATICS | STAR | AXB | GENERALIZED INVERSES | RANGE | Operators (mathematics) | Hilbert space | Mathematical analysis | Linear operators | Infimum

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 581, pp. 214 - 246

Given a bounded selfadjoint operator W on a Krein space H and a closed subspace S of H, the Schur complement of W to S is defined under the hypothesis of weak complementability...

Schur complements | Oblique projections | Krein spaces | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | Operators | Complement

Schur complements | Oblique projections | Krein spaces | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | Operators | Complement

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 02/2017, Volume 515, pp. 226 - 245

Given two subsets A and B of the algebra of bounded linear operators on a Hilbert space H we denote by AB:={AB:A∈A,B∈B...

Partial isometries | Projections | Factorizations | Polar decomposition | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | MATRICES | POSITIVE OPERATORS | HILBERT-SPACE | Algebra

Partial isometries | Projections | Factorizations | Polar decomposition | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | MATRICES | POSITIVE OPERATORS | HILBERT-SPACE | Algebra

Journal Article

Theoretical Chemistry Accounts, ISSN 1432-881X, 1/2012, Volume 131, Issue 1, pp. 1 - 20

.... Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained...

X2C method | Theoretical and Computational Chemistry | Chemistry | Relativistic electronic structure theory | Picture change error | Physical Chemistry | Douglas–Kroll–Hess method | Fock operator | Atomic/Molecular Structure and Spectra | Inorganic Chemistry | Organic Chemistry | Douglas-Kroll-Hess method | DIRAC-EQUATION | DENSITY-FUNCTIONAL CALCULATIONS | CHEMISTRY, PHYSICAL | REGULAR APPROXIMATION | NORMALIZED ELIMINATION | QUANTUM-CHEMISTRY | DOUGLAS-KROLL TRANSFORMATION | NONRELATIVISTIC METHODS | PROJECTION OPERATORS | HESS TRANSFORMATION | ELECTRON-DENSITY

X2C method | Theoretical and Computational Chemistry | Chemistry | Relativistic electronic structure theory | Picture change error | Physical Chemistry | Douglas–Kroll–Hess method | Fock operator | Atomic/Molecular Structure and Spectra | Inorganic Chemistry | Organic Chemistry | Douglas-Kroll-Hess method | DIRAC-EQUATION | DENSITY-FUNCTIONAL CALCULATIONS | CHEMISTRY, PHYSICAL | REGULAR APPROXIMATION | NORMALIZED ELIMINATION | QUANTUM-CHEMISTRY | DOUGLAS-KROLL TRANSFORMATION | NONRELATIVISTIC METHODS | PROJECTION OPERATORS | HESS TRANSFORMATION | ELECTRON-DENSITY

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2016, Volume 49, Issue 42, p. 425301

The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique...

perturbation expansion | projection operators | evolution operator | EQUATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Quantum Physics

perturbation expansion | projection operators | evolution operator | EQUATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Physics - Quantum Physics

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2019, Volume 577, pp. 134 - 158

Halmos' two projections theorem for Hilbert space operators is one of the fundamental results in operator theory...

Hilbert [formula omitted]-module | Orthogonal complement | Halmos' two projections theorem | Friedrichs angle | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert C-module | ADJOINTABLE OPERATORS | Operators | Theorems | Hilbert space | Modules

Hilbert [formula omitted]-module | Orthogonal complement | Halmos' two projections theorem | Friedrichs angle | MATHEMATICS | MATHEMATICS, APPLIED | Hilbert C-module | ADJOINTABLE OPERATORS | Operators | Theorems | Hilbert space | Modules

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2018, Volume 555, pp. 70 - 83

Let H be a Hilbert space and L(H) be the algebra of all bounded linear operators from H to H...

Factorization of operators | Orthogonal projections | Self-adjoint operators | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED

Factorization of operators | Orthogonal projections | Self-adjoint operators | MATHEMATICS | EQUATIONS | MATHEMATICS, APPLIED

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 6/2016, Volume 169, Issue 3, pp. 1042 - 1068

We introduce a first-order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method...

90C06 | Mathematics | Theory of Computation | First-order methods | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Cone programming | Operator splitting | 49M29 | 49M05 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | SETS | DECOMPOSITION | SYSTEMS | INVERSE | Electrical engineering | Computer science | Studies | Mathematical programming | Freeware | Operators | Splitting | Mathematical models | Subspaces | Intersections | Source code

90C06 | Mathematics | Theory of Computation | First-order methods | Optimization | Calculus of Variations and Optimal Control; Optimization | 90C25 | Cone programming | Operator splitting | 49M29 | 49M05 | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | PROJECTION | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | SETS | DECOMPOSITION | SYSTEMS | INVERSE | Electrical engineering | Computer science | Studies | Mathematical programming | Freeware | Operators | Splitting | Mathematical models | Subspaces | Intersections | Source code

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2015, Volume 421, Issue 1, pp. 1 - 20

We introduce regularity notions for averaged nonexpansive operators. Combined with regularity notions of their fixed point sets, we obtain linear and strong convergence results for quasicyclic, cyclic, and random iterations...

Douglas–Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Douglas–Rachford algorithm | Averaged nonexpansive mapping | Projection | Nonexpansive operator | Convex feasibility problem | Bounded linear regularity | Douglas-Rachford algorithm | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | PROJECTIONS | Analysis | Algorithms

Journal Article

Annals of Physics, ISSN 0003-4916, 2008, Volume 323, Issue 6, pp. 1502 - 1528

We show that Newton–Leibniz integration over Dirac’s ket-bra projection operators with continuum variables, which can be performed by the technique of integration within ordered product (IWOP) of operators...

Generalized Wigner operator | Bivariate-normal-distribution for normally ordered operators | Entangled Husimi operator | Entangled state representation | Integration for ket-bra operators | The IWOP technique | STATES | the IWOP technique | bivariate-normal-distribution for normally ordered operators | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | LIGHT | COHERENT | entangled state representation | integration for ket-bra operators | generalized Wigner operator | IWOP TECHNIQUE | OPTICS | entangled Husimi operator | Normal distribution | Quantum physics | PHASE SPACE | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS

Generalized Wigner operator | Bivariate-normal-distribution for normally ordered operators | Entangled Husimi operator | Entangled state representation | Integration for ket-bra operators | The IWOP technique | STATES | the IWOP technique | bivariate-normal-distribution for normally ordered operators | PHYSICS, MULTIDISCIPLINARY | MOMENTUM | LIGHT | COHERENT | entangled state representation | integration for ket-bra operators | generalized Wigner operator | IWOP TECHNIQUE | OPTICS | entangled Husimi operator | Normal distribution | Quantum physics | PHASE SPACE | PROJECTION OPERATORS | QUANTUM ENTANGLEMENT | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | STATISTICS

Journal Article

Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 14, pp. 4579 - 4585

A bounded operator Ton a finite or infinite-dimensional Hilbert space is called a disjoint range (DR) operator if R(T) boolean AND R(T*) = {0...

Moore-penrose inverse | CoR operators | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | ORTHOGONAL PROJECTIONS | HILBERT-SPACE | Moore-Penrose inverse

Moore-penrose inverse | CoR operators | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCTS | ORTHOGONAL PROJECTIONS | HILBERT-SPACE | Moore-Penrose inverse

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 09/2012, Volume 75, Issue 14, pp. 5448 - 5465

We introduce and study new classes of Bregman nonexpansive operators in reflexive Banach spaces...

Boltzmann–Shannon entropy | Bregman firmly nonexpansive operator | Nonexpansive operator | Reflexive Banach space | Resolvent | Retraction | Monotone mapping | [formula omitted]-monotone mapping | Legendre function | Bregman distance | Totally convex function | Fermi–Dirac entropy | T-monotone mapping | Fermi-Dirac entropy | Boltzmann-Shannon entropy | MATHEMATICS, APPLIED | ALGORITHM | MATHEMATICS | MAPPINGS | PROJECTIONS

Boltzmann–Shannon entropy | Bregman firmly nonexpansive operator | Nonexpansive operator | Reflexive Banach space | Resolvent | Retraction | Monotone mapping | [formula omitted]-monotone mapping | Legendre function | Bregman distance | Totally convex function | Fermi–Dirac entropy | T-monotone mapping | Fermi-Dirac entropy | Boltzmann-Shannon entropy | MATHEMATICS, APPLIED | ALGORITHM | MATHEMATICS | MAPPINGS | PROJECTIONS

Journal Article