Reviews in Mathematical Physics, ISSN 0129-055X, 07/2017, Volume 29, Issue 6, p. 1750021

As earlier conjectured by several authors and much later established by Solèr (relying on partial results by Piron, Maeda–Maeda and other authors), from the...

real spectral analysis | von Neumann algebras | representation theory | lattice theory | Poincaré group | quaternionic quantum mechanics | Real quantum mechanics | QUANTIQUE | Poincare group | PHYSICS, MATHEMATICAL

real spectral analysis | von Neumann algebras | representation theory | lattice theory | Poincaré group | quaternionic quantum mechanics | Real quantum mechanics | QUANTIQUE | Poincare group | PHYSICS, MATHEMATICAL

Journal Article

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY, ISSN 1812-9471, 2019, Volume 15, Issue 3, pp. 395 - 411

In this paper, we introduce and study the frames in separable quaternionic Hilbert spaces. The results on the existence of frames in quaternionic Hilbert...

MATHEMATICS | MATHEMATICS, APPLIED | quaternionic Hilbert spaces | PHYSICS, MATHEMATICAL | frame

MATHEMATICS | MATHEMATICS, APPLIED | quaternionic Hilbert spaces | PHYSICS, MATHEMATICAL | frame

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 05/2013, Volume 25, Issue 4, p. 1350006

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical...

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

Slice regular functions | Operator algebras | Spectral theory | Non-commutative functional calculus | Quaternionic quantum mechanics | Continuous functional calculus C | algebras | Quaternionic Hilbert space | slice regular functions | spectral theory | C-algebras | QUANTIQUE | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL | non-commutative functional calculus | continuous functional calculus | ALGEBRAS | operator algebras | QUANTUM-MECHANICS | quaternionic quantum mechanics

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 05/2019, Volume 31, Issue 4, p. 1950013

As earlier conjectured by several authors and much later established by Solèr, from the lattice-theory point of view, Quantum Mechanics may be formulated in...

representation theory | Foundation of quantum mechanics | spectral theory | quaternionic functional analysis | PHYSICS, MATHEMATICAL

representation theory | Foundation of quantum mechanics | spectral theory | quaternionic functional analysis | PHYSICS, MATHEMATICAL

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 2/2020, Volume 30, Issue 1, pp. 1 - 9

In this paper, we prove some inequalities between quaternionic bounded selfadjoint operators on quaternionic Hilbert spaces. We follow the Mond–Pečaric̀ method...

Mond–Pečaric̀ method | Mathematical Methods in Physics | Continuous functional calculus | Spectral theory | Theoretical, Mathematical and Computational Physics | 47A99 | Applications of Mathematics | Physics, general | 47A63 | Physics | Quaternionic Hilbert spaces

Mond–Pečaric̀ method | Mathematical Methods in Physics | Continuous functional calculus | Spectral theory | Theoretical, Mathematical and Computational Physics | 47A99 | Applications of Mathematics | Physics, general | 47A63 | Physics | Quaternionic Hilbert spaces

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2018, Volume 112, Issue 4, pp. 1049 - 1057

In this paper we consider the new concept of the quaternionic unitary representation of a locally compact group to the unitary group of a quaternionic Hilbert...

47B07 | 46E22 | Theoretical, Mathematical and Computational Physics | Continuous wavelet transform | Mathematics, general | Unitary representation | 47A67 | Mathematics | Quaternionic Hilbert space | Applications of Mathematics | MATHEMATICS

47B07 | 46E22 | Theoretical, Mathematical and Computational Physics | Continuous wavelet transform | Mathematics, general | Unitary representation | 47A67 | Mathematics | Quaternionic Hilbert space | Applications of Mathematics | MATHEMATICS

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 2/2019, Volume 29, Issue 1, pp. 1 - 10

In this paper, we study weak topology on right quaternionic Hilbert spaces. We show that on right quaternionic Hilbert spaces weak compactness and weak...

47B07 | Mathematical Methods in Physics | 46E22 | Theoretical, Mathematical and Computational Physics | Weak topology | Compact operators | Applications of Mathematics | Physics, general | Physics | Quaternionic Hilbert spaces | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

47B07 | Mathematical Methods in Physics | 46E22 | Theoretical, Mathematical and Computational Physics | Weak topology | Compact operators | Applications of Mathematics | Physics, general | Physics | Quaternionic Hilbert spaces | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 01/2019, Volume 135, pp. 7 - 20

In this note first we study the Weyl operators and Weyl S-spectrum of a bounded right quaternionic linear operator, in the setting of the so-called S-spectrum,...

S-spectrum | Weyl S-spectrum | Quaternions | Browder operator | Quaternionic Hilbert spaces | MATHEMATICS | PHYSICS, MATHEMATICAL | OPERATORS | Computer science

S-spectrum | Weyl S-spectrum | Quaternions | Browder operator | Quaternionic Hilbert spaces | MATHEMATICS | PHYSICS, MATHEMATICAL | OPERATORS | Computer science

Journal Article

Thai Journal of Mathematics, ISSN 1686-0209, 2017, Volume 15, Issue 2, pp. 475 - 482

Journal Article

Reviews in Mathematical Physics, ISSN 0129-055X, 11/2017, Volume 29, Issue 10, p. 1750034

The possibility of formulating quantum mechanics over quaternionic Hilbert spaces can be traced back to von Neumann’s foundational works in the thirties. The...

quaternionic PVMs | Quaternionic functional analysis | quaternionic spectral theorem for normal unbounded operators | quantum mechanics in quaternionic Hilbert space | THEOREM | QUANTIQUE | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | UNITARY OPERATORS

quaternionic PVMs | Quaternionic functional analysis | quaternionic spectral theorem for normal unbounded operators | quantum mechanics in quaternionic Hilbert space | THEOREM | QUANTIQUE | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | UNITARY OPERATORS

Journal Article

Foundations of Physics, ISSN 0015-9018, 5/2013, Volume 43, Issue 5, pp. 656 - 664

We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on...

Philosophy of Science | Born rule | Quantum Physics | Quantum foundations | Statistical Physics, Dynamical Systems and Complexity | Physics | History and Philosophical Foundations of Physics | Quaternions | Quaternionic POVMs | Quaternionic quantum channels | Mechanics | Division rings | Classical and Quantum Gravitation, Relativity Theory | MECHANICS | GLEASON | PHYSICS, MULTIDISCIPLINARY | THEOREM | Hilbert space | Research | Quantum theory | Mathematical physics | Physics - Quantum Physics

Philosophy of Science | Born rule | Quantum Physics | Quantum foundations | Statistical Physics, Dynamical Systems and Complexity | Physics | History and Philosophical Foundations of Physics | Quaternions | Quaternionic POVMs | Quaternionic quantum channels | Mechanics | Division rings | Classical and Quantum Gravitation, Relativity Theory | MECHANICS | GLEASON | PHYSICS, MULTIDISCIPLINARY | THEOREM | Hilbert space | Research | Quantum theory | Mathematical physics | Physics - Quantum Physics

Journal Article

Annals of Functional Analysis, ISSN 2008-8752, 2015, Volume 6, Issue 4, pp. 226 - 246

In this article, we study the geometry and operator theory on quaternionic Hilbert spaces. As it is well-known, Cowen Douglas operators are a class of...

Cowen-Douglas operator | Quaternionic hilbert space | Unitary equivalence | Holomorphic curve | MATHEMATICS | quaternionic Hilbert space | MATHEMATICS, APPLIED | unitary equivalence | holomorphic curve | QUANTUM-MECHANICS

Cowen-Douglas operator | Quaternionic hilbert space | Unitary equivalence | Holomorphic curve | MATHEMATICS | quaternionic Hilbert space | MATHEMATICS, APPLIED | unitary equivalence | holomorphic curve | QUANTUM-MECHANICS

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 06/2012, Volume 57, Issue 6, pp. 667 - 675

We show that Drury's proof of the generalisation of the von Neumann inequality to the case of contractive rows of N-tuples of commuting operators still holds...

Secondary 46A32 | Primary 47A60 | von Neumann inequality | tensor products | 47B32 | 47S10 | quaternionic Hilbert spaces | reproducing kernel Hilbert spaces | Drury-Arveson space | MATHEMATICS | BALL | PRODUCT | Estimates | Cybernetics | Quantum theory | Inequality | Operators | Tensors | Mathematical analysis | Inequalities | Proving | Hilbert space | Complex variables

Secondary 46A32 | Primary 47A60 | von Neumann inequality | tensor products | 47B32 | 47S10 | quaternionic Hilbert spaces | reproducing kernel Hilbert spaces | Drury-Arveson space | MATHEMATICS | BALL | PRODUCT | Estimates | Cybernetics | Quantum theory | Inequality | Operators | Tensors | Mathematical analysis | Inequalities | Proving | Hilbert space | Complex variables

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 12/2017, Volume 27, Issue 4, pp. 2933 - 2960

The Cimmino system offers a natural and elegant generalization to four-dimensional case of the Cauchy–Riemann system of first order complex partial...

Secondary 32A40 | Quaternionic analysis | Cimmino system | Hilbert formulas | Mathematical Methods in Physics | Poincaré–Bertrand formula | Theoretical, Mathematical and Computational Physics | Primary 30G35 | Applications of Mathematics | Physics, general | Physics | SYSTEM | MATHEMATICS, APPLIED | TRANSPORT-THEORY | PHYSICS, MATHEMATICAL | Poincare-Bertrand formula | UNIT-SPHERE | Analysis | Differential equations

Secondary 32A40 | Quaternionic analysis | Cimmino system | Hilbert formulas | Mathematical Methods in Physics | Poincaré–Bertrand formula | Theoretical, Mathematical and Computational Physics | Primary 30G35 | Applications of Mathematics | Physics, general | Physics | SYSTEM | MATHEMATICS, APPLIED | TRANSPORT-THEORY | PHYSICS, MATHEMATICAL | Poincare-Bertrand formula | UNIT-SPHERE | Analysis | Differential equations

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 416, Issue 2, pp. 580 - 587

We solve the problem of finding the best possible constant of ultraprimeness for the special class of Euclidean algebra called algebra of hermitian operators...

Quaternionic Hilbert space | Spectral norm | Jacobson–McCrimmon operator | Euclidean algebras | Ultraprime algebras | Jacobson-McCrimmon operator

Quaternionic Hilbert space | Spectral norm | Jacobson–McCrimmon operator | Euclidean algebras | Ultraprime algebras | Jacobson-McCrimmon operator

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2020, pp. 1 - 25

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2017, Volume 27, Issue 1, pp. 87 - 98

We study the Hilbert boundary value problem with Fermionic weight for the Dirac operator on smooth surfaces of $${\mathbb{R}^{3}}$$ R 3 . We give the solution...

Quaternionic analysis | Mathematical Methods in Physics | 32A25 | Hilbert boundary value problems | Theoretical, Mathematical and Computational Physics | 58A10 | 30G35 | Applications of Mathematics | Physics, general | Dirac operator | Physics | MATHEMATICS, APPLIED | DISCRETE | ISING-MODEL | DIRAC OPERATORS | PHYSICS, MATHEMATICAL | GRAPHS

Quaternionic analysis | Mathematical Methods in Physics | 32A25 | Hilbert boundary value problems | Theoretical, Mathematical and Computational Physics | 58A10 | 30G35 | Applications of Mathematics | Physics, general | Dirac operator | Physics | MATHEMATICS, APPLIED | DISCRETE | ISING-MODEL | DIRAC OPERATORS | PHYSICS, MATHEMATICAL | GRAPHS

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 02/2019, Volume 13, Issue 1, pp. 85 - 113

In this paper we define the deficiency indices of a closed symmetric right H-linear operator and formulate a general theory of deficiency indices in a right...

S-spectrum | Symmetric operator | Deficiency index | Quaternions | Quaternionic Hilbert spaces | MATHEMATICS | MATHEMATICS, APPLIED | Computer science

S-spectrum | Symmetric operator | Deficiency index | Quaternions | Quaternionic Hilbert spaces | MATHEMATICS | MATHEMATICS, APPLIED | Computer science

Journal Article

Mathematische Nachrichten, ISSN 0025-584X, 12/2017, Volume 290, Issue 17-18, pp. 2725 - 2739

In this paper we introduce and study the fractional Hardy spaces of the half space and of the unit ball in the quaternionic setting. In particular, we discuss...

30G35 | unit ball | half space | Quaternionic fractional Hardy spaces | 30H10 | Unit ball | Half space | MATHEMATICS

30G35 | unit ball | half space | Quaternionic fractional Hardy spaces | 30H10 | Unit ball | Half space | MATHEMATICS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 01/2018, Volume 124, pp. 442 - 455

In this paper we define the quaternionic Cayley transformation of a densely defined, symmetric, quaternionic right linear operator and formulate a general...

S-spectrum | Symmetric operator | Quaternions | Cayley transform | Quaternionic Hilbert spaces | MATHEMATICS | Quatemionic Hilbert spaces | PHYSICS, MATHEMATICAL | Computer science

S-spectrum | Symmetric operator | Quaternions | Cayley transform | Quaternionic Hilbert spaces | MATHEMATICS | Quatemionic Hilbert spaces | PHYSICS, MATHEMATICAL | Computer science

Journal Article

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