Memoirs of the American Mathematical Society, ISSN 0065-9266, 05/2010, Volume 205, Issue 964, pp. 1 - 130

Cauchy transform | Commutant lifting | Fock space | Invariant subspace | Hardy algebra | Weighted shifts | Noncommutative domain | Free holomorphic function | Von Neumann inequality | Functional calculus | Wold decomposition | Characteristic function | Interpolation | Noncommutative variety | Model theory | Dilation | Multivariable operator theory | Curvature | Poisson transform | Bohr inequality | CURVATURE INVARIANT | ISOMETRIC DILATIONS | MATHEMATICS | POWER-SERIES | INTERPOLATION PROBLEMS | FREE SEMIGROUP ALGEBRAS | ASTERISK-CORRESPONDENCES | POISSON TRANSFORMS | ANALYTIC TOEPLITZ ALGEBRAS | UNIT BALL | FOCK SPACES

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 1/2013, Volume 75, Issue 1, pp. 87 - 133

In this paper, we study noncommutative domains $${\mathbb{D}_f^\varphi(\mathcal{H}) \subset B(\mathcal{H})^n}$$ generated by positive regular free holomorphic...

weighted Fock space | 46T25 | 46L07 | noncommutative Reinhardt domain | invariant subspace | 47A45 | Mathematics | noncommutative Poisson transform | Secondary 47A20 | operator model theory | Analysis | Nevanlinna-Pick interpolation | commutant lifting | Multivariable operator theory | characteristic function | Primary 46L52 | free biholomorphic function | INTERPOLATION | MATHEMATICS

weighted Fock space | 46T25 | 46L07 | noncommutative Reinhardt domain | invariant subspace | 47A45 | Mathematics | noncommutative Poisson transform | Secondary 47A20 | operator model theory | Analysis | Nevanlinna-Pick interpolation | commutant lifting | Multivariable operator theory | characteristic function | Primary 46L52 | free biholomorphic function | INTERPOLATION | MATHEMATICS

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2006, Volume 55, Issue 2, pp. 389 - 442

We develop a dilation theory on noncommutative varieties determined by row contractions T := [T1,...,Tn] subject to constraints such as p(T1,...,Tn) = 0, p ∈...

Interpolation | Algebra | Mathematical theorems | Eigenfunctions | Hilbert spaces | Polynomials | Mathematical inequalities | Curvature | Factorization | Commutant lifting | Fock space | Invariant subspace | Von Neumann inequality | Row contraction | Wold decomposition | Noncommutative variety | Poisson kernel | Constrained shift | Multivariable operator theory | Dilation the-ory | Char-acteristic function | FUNCTIONAL-CALCULUS | dilation theory | REPRESENTATIONS | invariant subspace | noncommutative variety | CURVATURE INVARIANT | ISOMETRIC DILATIONS | MATHEMATICS | constrained shift | interpolation | von Neumann inequality | INFINITE SEQUENCES | N-TUPLES | commutant lifting | POISSON TRANSFORMS | TENSOR-ALGEBRAS | row contraction | Weld decomposition | characteristic function | ANALYTIC TOEPLITZ ALGEBRAS | multivariable operator theory

Interpolation | Algebra | Mathematical theorems | Eigenfunctions | Hilbert spaces | Polynomials | Mathematical inequalities | Curvature | Factorization | Commutant lifting | Fock space | Invariant subspace | Von Neumann inequality | Row contraction | Wold decomposition | Noncommutative variety | Poisson kernel | Constrained shift | Multivariable operator theory | Dilation the-ory | Char-acteristic function | FUNCTIONAL-CALCULUS | dilation theory | REPRESENTATIONS | invariant subspace | noncommutative variety | CURVATURE INVARIANT | ISOMETRIC DILATIONS | MATHEMATICS | constrained shift | interpolation | von Neumann inequality | INFINITE SEQUENCES | N-TUPLES | commutant lifting | POISSON TRANSFORMS | TENSOR-ALGEBRAS | row contraction | Weld decomposition | characteristic function | ANALYTIC TOEPLITZ ALGEBRAS | multivariable operator theory

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2014, Volume 16, Issue 5, pp. 1350034 - 1-1350034-49

We obtain all Dirichlet spaces ℱq, q ∈ ℝ, of holomorphic functions on the unit ball of ℂN as weighted symmetric Fock spaces over ℂN. We develop the basics of...

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | MATHEMATICS, APPLIED | BESOV-SPACES | DIRICHLET SPACES | INTERPOLATION | MATHEMATICS | ALGEBRAS | BERGMAN SPACES | BALL | TOEPLITZ-OPERATORS | STANDARD MODELS | HILBERT-SPACE | C-algebra | Functions (mathematics) | Operators | Algebra | Mathematical analysis | Inequalities | Multivariable | Dirichlet problem | Touch

extension | analytic Hilbert module | radial differential operator | Toeplitz | multiplier | shift | virtual point | Bergman | Hardy | short exact sequence | Drury-Arveson | Fock | von Neumann inequality | Busby invariant | spectrum | Fredholm | subnormal | K-groups | Dirichlet | reproducing kernel Hilbert space | commutant | C∗-algebra | hyponormal | row contraction | MATHEMATICS, APPLIED | BESOV-SPACES | DIRICHLET SPACES | INTERPOLATION | MATHEMATICS | ALGEBRAS | BERGMAN SPACES | BALL | TOEPLITZ-OPERATORS | STANDARD MODELS | HILBERT-SPACE | C-algebra | Functions (mathematics) | Operators | Algebra | Mathematical analysis | Inequalities | Multivariable | Dirichlet problem | Touch

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 07/2007, Volume 135, Issue 7, pp. 2151 - 2164

An n-tuple of operators T:=[T_1,\ldots, T_n] on a Hilbert space \mathcal{H} is called a J-constrained row contraction if T_1T_1^*+\cdots + T_nT_n^*\leq...

Algebra | Model theory | Eigenfunctions | Hilbert spaces | Polynomials | Mathematical inequalities | Commuting | Preprints | Operator theory | Characteristic function | Noncommutative variety | Poisson kernel | Fock space | Constrained shift | Von neumann inequality | Multivariable operator theory | Unitary invariant | Row contraction | FUNCTIONAL-CALCULUS | unitary invariant | TUPLES | MATHEMATICS, APPLIED | model theory | noncommutative variety | INTERPOLATION | MATHEMATICS | constrained shift | ALGEBRAS | von Neumann inequality | MULTI-ANALYTIC OPERATORS | INFINITE SEQUENCES | MODELS | POISSON TRANSFORMS | row contraction | characteristic function | multivariable operator theory

Algebra | Model theory | Eigenfunctions | Hilbert spaces | Polynomials | Mathematical inequalities | Commuting | Preprints | Operator theory | Characteristic function | Noncommutative variety | Poisson kernel | Fock space | Constrained shift | Von neumann inequality | Multivariable operator theory | Unitary invariant | Row contraction | FUNCTIONAL-CALCULUS | unitary invariant | TUPLES | MATHEMATICS, APPLIED | model theory | noncommutative variety | INTERPOLATION | MATHEMATICS | constrained shift | ALGEBRAS | von Neumann inequality | MULTI-ANALYTIC OPERATORS | INFINITE SEQUENCES | MODELS | POISSON TRANSFORMS | row contraction | characteristic function | multivariable operator theory

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 2/2019, Volume 91, Issue 1, pp. 1 - 55

The goal of this paper is to study the Bohr phenomenon in the setting of free holomorphic functions on noncommutative regular polydomains $$\mathbf{D_f^m}$$...

Noncommutative polydomain | 46L52 | Bohr’s inequality | Weighted Fock space | Analysis | Primary 47A56 | Secondary 32A38 | Free holomorphic function | Berezin transform | Mathematics | Multivariable operator theory | 47A63 | MATHEMATICS | RADIUS | Bohr's inequality | THEOREM | TRANSFORMS

Noncommutative polydomain | 46L52 | Bohr’s inequality | Weighted Fock space | Analysis | Primary 47A56 | Secondary 32A38 | Free holomorphic function | Berezin transform | Mathematics | Multivariable operator theory | 47A63 | MATHEMATICS | RADIUS | Bohr's inequality | THEOREM | TRANSFORMS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 1, pp. 256 - 293

We initiate the study of weighted multi-Toeplitz operators associated with noncommutative regular domains , , where is the algebra of all bounded linear...

Free pluriharmonic function | Noncommutative domain | Multi-Toeplitz operator | Berezin transform | Multivariable operator theory | Full Fock space | MATHEMATICS, APPLIED | REPRESENTATIONS | ANALYTIC OPERATORS | MATHEMATICS | ALGEBRAS | ASTERISK-CORRESPONDENCES | TRANSFORMS

Free pluriharmonic function | Noncommutative domain | Multi-Toeplitz operator | Berezin transform | Multivariable operator theory | Full Fock space | MATHEMATICS, APPLIED | REPRESENTATIONS | ANALYTIC OPERATORS | MATHEMATICS | ALGEBRAS | ASTERISK-CORRESPONDENCES | TRANSFORMS

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 10/2018, Volume 90, Issue 5, pp. 1 - 17

Let $$H_m({\mathbb {B}})$$ Hm(B) be the analytic functional Hilbert space on the unit ball $${\mathbb {B}} \subset {\mathbb {C}}^n$$ B⊂Cn with reproducing...

Secondary 47A45 | 46E22 | Analysis | 47B32 | Mathematics | Primary 47A13 | Multivariable Bergman shifts | Wold decomposition | Analytic models | MATHEMATICS | TUPLES | HYPERCONTRACTIONS | SUBSPACES | OPERATORS | ISOMETRIES

Secondary 47A45 | 46E22 | Analysis | 47B32 | Mathematics | Primary 47A13 | Multivariable Bergman shifts | Wold decomposition | Analytic models | MATHEMATICS | TUPLES | HYPERCONTRACTIONS | SUBSPACES | OPERATORS | ISOMETRIES

Journal Article

Journal of Operator Theory, ISSN 0379-4024, 10/2012, Volume 68, Issue 2, pp. 307 - 334

This is a retrospective of some of William Arveson's many contributions to operator theory and operator algebras.

Operator algebras | Von Neumann algebra | Algebra | Mathematical theorems | Mathematical lattices | Hilbert spaces | Mathematical functions | Commuting | Operator theory | Automorphism groups | Dilation theory | Invariant subspaces | Commutative subspace lattices | Nest algebras | Maximal subdiagonal operator algebras | Completely positive maps | Multivariable operator theory | Dynamical systems | REPRESENTATIONS | THEOREM | CSTAR-ALGEBRAS | completely positive maps | SIMILARITY PROBLEM | automorphism groups | maximal subdiagonal operator algebras | SUBALGEBRAS | commutative subspace lattices | POLYNOMIALLY BOUNDED OPERATOR | INTERPOLATION | MATHEMATICS | dynamical systems | ANALYTIC FUNCTIONS | MODELS | invariant subspaces | nest algebras | multivariable operator theory

Operator algebras | Von Neumann algebra | Algebra | Mathematical theorems | Mathematical lattices | Hilbert spaces | Mathematical functions | Commuting | Operator theory | Automorphism groups | Dilation theory | Invariant subspaces | Commutative subspace lattices | Nest algebras | Maximal subdiagonal operator algebras | Completely positive maps | Multivariable operator theory | Dynamical systems | REPRESENTATIONS | THEOREM | CSTAR-ALGEBRAS | completely positive maps | SIMILARITY PROBLEM | automorphism groups | maximal subdiagonal operator algebras | SUBALGEBRAS | commutative subspace lattices | POLYNOMIALLY BOUNDED OPERATOR | INTERPOLATION | MATHEMATICS | dynamical systems | ANALYTIC FUNCTIONS | MODELS | invariant subspaces | nest algebras | multivariable operator theory

Journal Article

2007, 2nd ed., Systems & control., ISBN 9780817645816, xxvi, 575

Book

Journal of Functional Analysis, ISSN 0022-1236, 06/2019, Volume 276, Issue 11, pp. 3406 - 3440

A noncommutative domain , , of -tuples of bounded linear operators on a Hilbert space is associated with any positive regular free holomorphic function . If is...

Noncommutative variety | Invariant subspace | Fock space | Multivariable operator theory | Wandering subspace | Noncommutative hyperball | Inner function | OPERATOR-THEORY | THEOREM | MATHEMATICS | INVARIANT SUBSPACES | STANDARD MODELS | BEREZIN TRANSFORMS

Noncommutative variety | Invariant subspace | Fock space | Multivariable operator theory | Wandering subspace | Noncommutative hyperball | Inner function | OPERATOR-THEORY | THEOREM | MATHEMATICS | INVARIANT SUBSPACES | STANDARD MODELS | BEREZIN TRANSFORMS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2008, Volume 254, Issue 4, pp. 1003 - 1057

In this paper, we initiate the study of a class of noncommutative domains of -tuples of bounded linear operators on a Hilbert space , where , , and is a...

Noncommutative variety | Dilation theory | Fock space | von Neumann inequality | Model theory | Noncommutative domain | Weighted shift | Berezin transform | Multivariable operator theory | Creation operators | Wold decomposition | CURVATURE INVARIANT | ISOMETRIC DILATIONS | INTERPOLATION | MATHEMATICS | INFINITE SEQUENCES | N-TUPLES | FREE SEMIGROUP ALGEBRAS | HYPERCONTRACTIONS | STANDARD MODELS | POISSON TRANSFORMS | ANALYTIC TOEPLITZ ALGEBRAS

Noncommutative variety | Dilation theory | Fock space | von Neumann inequality | Model theory | Noncommutative domain | Weighted shift | Berezin transform | Multivariable operator theory | Creation operators | Wold decomposition | CURVATURE INVARIANT | ISOMETRIC DILATIONS | INTERPOLATION | MATHEMATICS | INFINITE SEQUENCES | N-TUPLES | FREE SEMIGROUP ALGEBRAS | HYPERCONTRACTIONS | STANDARD MODELS | POISSON TRANSFORMS | ANALYTIC TOEPLITZ ALGEBRAS

Journal Article

MONATSHEFTE FUR MATHEMATIK, ISSN 0026-9255, 06/2019, Volume 189, Issue 2, pp. 377 - 381

In this brief note, we show that the hypotheses of Lowner's theorem on matrix monotonicity in several commuting variables as proved by Agler, and Young can be...

Matrix montone functions | MATHEMATICS | Lowner's theorem | Multivariable operator theory | Commutative functional calculus

Matrix montone functions | MATHEMATICS | Lowner's theorem | Multivariable operator theory | Commutative functional calculus

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 1002 - 1053

Multivariable operator theory is used to provide Bohr inequalities for free holomorphic functions with operator coefficients on the regular polyball , , which...

Free pluriharmonic function | Free holomorphic function | Berezin transform | Multivariable operator theory | Bohr's inequality | Noncommutative polyball | MATHEMATICS | Free pluriharrnonic function | RADIUS | THEOREM | TRANSFORMS | Analysis | Algebra

Free pluriharmonic function | Free holomorphic function | Berezin transform | Multivariable operator theory | Bohr's inequality | Noncommutative polyball | MATHEMATICS | Free pluriharrnonic function | RADIUS | THEOREM | TRANSFORMS | Analysis | Algebra

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2016, Volume 368, Issue 6, pp. 4357 - 4416

This paper is an attempt to unify the multivariable operator model theory for ball-like domains and commutative polydiscs and extend it to a more general class...

Characteristic function | Noncommutative polydomain | Dilation theory | Fock space | Invariant subspace | Berezin transform | Free holomorphic function | Weighted shift | Multivariable operator theory | Functional calculus

Characteristic function | Noncommutative polydomain | Dilation theory | Fock space | Invariant subspace | Berezin transform | Free holomorphic function | Weighted shift | Multivariable operator theory | Functional calculus

Journal Article

1997, Mathematics and its applications, ISBN 0792346831, Volume 419, 500., 2 v.

Book

Journal of Functional Analysis, ISSN 0022-1236, 12/2014, Volume 267, Issue 11, pp. 4446 - 4498

In this paper we consider several problems of joint similarity to tuples of bounded linear operators in noncommutative polydomains and varieties associated...

Berezin transform | Multivariable operator theory | Fock space | Similarity | POLYNOMIALLY BOUNDED OPERATOR | MATHEMATICS | ALGEBRAS | JOINT SIMILARITY | TRANSFORMS | Analysis | Algebra

Berezin transform | Multivariable operator theory | Fock space | Similarity | POLYNOMIALLY BOUNDED OPERATOR | MATHEMATICS | ALGEBRAS | JOINT SIMILARITY | TRANSFORMS | Analysis | Algebra

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2013, Volume 265, Issue 10, pp. 2500 - 2552

Let be a set of polynomials in noncommutative indeterminates , , . In this paper, we study noncommutative varieties where is a in and is the algebra of bounded...

Noncommutative polydomain | Characteristic function | Noncommutative variety | Dilation theory | Fock space | Invariant subspace | Berezin transform | Free holomorphic function | Multivariable operator theory | POLYDISK | INTERPOLATION | MATHEMATICS | ALGEBRAS | STANDARD OPERATOR MODELS | POISSON TRANSFORMS | Analysis | Algebra

Noncommutative polydomain | Characteristic function | Noncommutative variety | Dilation theory | Fock space | Invariant subspace | Berezin transform | Free holomorphic function | Multivariable operator theory | POLYDISK | INTERPOLATION | MATHEMATICS | ALGEBRAS | STANDARD OPERATOR MODELS | POISSON TRANSFORMS | Analysis | Algebra

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 6/2019, Volume 189, Issue 2, pp. 377 - 381

In this brief note, we show that the hypotheses of Löwner’s theorem on matrix monotonicity in several commuting variables as proved by Agler, and Young can be...

Matrix montone functions | Secondary 32A40 | Primary 47A63 | Mathematics, general | Mathematics | Multivariable operator theory | Commutative functional calculus | Löwner’s theorem

Matrix montone functions | Secondary 32A40 | Primary 47A63 | Mathematics, general | Mathematics | Multivariable operator theory | Commutative functional calculus | Löwner’s theorem

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2003, Volume 52, Issue 6, pp. 1595 - 1614

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these...

Integers | Standard basis vectors | Operator algebras | Algebra | Periodicity | Hilbert spaces | Semigroups | Operator theory | Projection of vectors | Operator | Fock space | Nonselfadjoint operator algebras | Noncommutative multivariable operator theory | Bilateral weighted shift | Hilbert space | Reducing subspaces | Infinite word | noncommutative multivariable operator theory | FACTORIZATION | REPRESENTATIONS | FREE SEMIGROUP ALGEBRAS | infinite word | nonselfadjoint operator algebras | operator | ISOMETRIC DILATIONS | MATHEMATICS | INFINITE SEQUENCES | N-TUPLES | REFLEXIVITY | MODELS | reducing subspaces | periodicity | bilateral weighted shift | ANALYTIC TOEPLITZ ALGEBRAS | FOCK SPACES

Integers | Standard basis vectors | Operator algebras | Algebra | Periodicity | Hilbert spaces | Semigroups | Operator theory | Projection of vectors | Operator | Fock space | Nonselfadjoint operator algebras | Noncommutative multivariable operator theory | Bilateral weighted shift | Hilbert space | Reducing subspaces | Infinite word | noncommutative multivariable operator theory | FACTORIZATION | REPRESENTATIONS | FREE SEMIGROUP ALGEBRAS | infinite word | nonselfadjoint operator algebras | operator | ISOMETRIC DILATIONS | MATHEMATICS | INFINITE SEQUENCES | N-TUPLES | REFLEXIVITY | MODELS | reducing subspaces | periodicity | bilateral weighted shift | ANALYTIC TOEPLITZ ALGEBRAS | FOCK SPACES

Journal Article

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