An invitation to the Drury-Arveson space

DOI10.1007/978-3-031-33572-3_10MaRDI QIDQ6613354

Michael Hartz

Publication date: 2 October 2024

zbMATH Keywords

dilationreproducing kernelFock spaceDrury-Arveson spaceNevanlinna-Pick interpolationmultivariable operator theorycomplete Pick space

Mathematics Subject Classification ID

Several-variable operator theory (spectral, Fredholm, etc.) (47A13) Abstract operator algebras on Hilbert spaces (47L30) Dilations, extensions, compressions of linear operators (47A20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (4)

Simply interpolating sequences in complete Pick spaces ⋮ Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball ⋮ Random Carleson sequences for the Hardy space on the polydisc and the unit ball ⋮ Non-commutative function theory and free probability. Abstracts from the workshop held April 28 -- May 3, 2024

Cites Work

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• An analytic Grothendieck Riemann Roch theorem
• A remark on the multipliers on spaces of weak products of functions
• Absolute continuity for commuting row contractions
• Nevanlinna-Pick interpolation and factorization of linear functionals
• Essential normality of homogeneous submodules
• The isomorphism problem for some universal operator algebras
• The Douglas property for multiplier algebras of operators
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• Noncommutative reproducing kernel Hilbert spaces
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• On bounded bilinear forms
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• Function theory in the unit ball of \({\mathbb{C}}^ n\)
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• Models for noncommuting operators
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• Interpolation problems in nest algebras
• Factorization theorems for Hardy spaces in several variables
• A characterization of Douglas subalgebras
• Subalgebras of \(L^\infty\) containing \(H^\infty\)
• Models for commuting contractions
• Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras
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• Complete Nevanlinna-Pick kernels
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• The Dirac operator of a commuting \(d\)-tuple.
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• On the isomorphism question for complete Pick multiplier algebras
• Noncommutative interpolation and Poisson transforms
• Dilation theory: a guided tour
• Paley-Wiener theorems on the Siegel upper half-space
• Embedding dimension of the Dirichlet space
• Multiplier tests and subhomogeneity of multiplier algebras
• Von Neumann's inequality for row contractive matrix tuples
• Multipliers and operator space structure of weak product spaces
• Weak products of Dirichlet functions
• Erratum to: ``Multipliers of embedded discs
• Radially weighted Besov spaces and the Pick property
• Interlacing families. II: Mixed characteristic polynomials and the Kadison-Singer problem
• Geometric Arveson-Douglas conjecture
• Factorization of analytic functions and operator inequalities
• On the preceding paper by R.\,B.\thinspace Leech
• Essentially normal Hilbert modules and \(K\)-homology
• Subalgebras of \(C^ *\)-algebras
• Subalgebras of C\(^*\)-algebras. II
• \(H^p\) spaces of several variables
• Interpolations by bounded analytic functions and the corona problem
• Harmonic analysis of operators on Hilbert space
• Spherical contractions and interpolation problems on the unit ball
• Hankel operators, invariant subspaces, and cyclic vectors in the Drury-Arveson space
• An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
• Foundations of Free Noncommutative Function Theory
• On the problem of characterizing multipliers for the Drury-Arveson space
• Isometric Dilations for Infinite Sequences of Noncommuting Operators
• An Interpolation Problem for Bounded Analytic Functions
• An $H^p$ scale for complete Pick spaces
• Theory of Bergman Spaces in the Unit Ball of C^n
• Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients
• Commutant lifting for commuting row contractions
• Invariant Subspaces and Hyper-Reflexivity for Free Semigroup Algebras
• A Note on Strictly Cyclic Weighted Shifts
• Von Neumann inequality for $(B(\mathscr{H})^n)_1$.
• Interpolation by Multipliers of the Dirichlet Space
• Standard Models for some Commuting Multioperators
• A Generalization of Von Neumann's Inequality to the Complex Ball

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