Holomorphic Kernels and Commuting Operators

DOI10.2307/2000706zbMath0675.47003OpenAlexW4232632346MaRDI QIDQ3830047

Ameer Athavale

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000706

zbMATH Keywords

Hardy spaceBergman spacekernelpositive definiteoperator polynomialscommuting normal extension*-dilation*- representation of the adjoint of a multiplication operator on the tensor product of functional Hilbert spacesm commuting operatorsregular analytic model atom

Mathematics Subject Classification ID

Subnormal operators, hyponormal operators, etc. (47B20) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Dilations, extensions, compressions of linear operators (47A20) Linear operators on function spaces (general) (47B38) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Tensor products in functional analysis (46M05)

Related Items (16)

Toeplitz algebras, subnormal tuples and rigidity on reproducing \(C[z_{1},\dots ,z_{d}\)-modules] ⋮ Bargmann-type kernels and unbounded subnormals ⋮ Applications of Hilbert Module Approach to Multivariable Operator Theory ⋮ Commutative Dilation Theory ⋮ Operators Cauchy dual to 2-hyperexpansive operators: the multivariable case ⋮ Berezin transforms on noncommutative varieties in polydomains ⋮ Moment problems and subnormality ⋮ Towards a Functional Calculus for Subnormal Tuples: The Minimal Normal Extension ⋮ Contractive Hilbert modules and their dilations ⋮ On completely hyperexpansive operators ⋮ Berezin transforms on noncommutative polydomains ⋮ On the sum of two subnormal kernels ⋮ An operator-valued Poisson kernel ⋮ Moment problems for multi-sequences of operators ⋮ On an intertwining lifting theorem for certain reproducing kernel Hilbert spaces ⋮ Analytic models for commuting operator tuples on bounded symmetric domains

Cites Work

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• The Arveson extension theorem and coanalytic models
• On linear functional operations and the moment problem for a finite interval in one or several dimensions
• Subalgebras of \(C^ *\)-algebras
• Subnormal operators
• Dilations on Involution Semigroups
• Theory of Reproducing Kernels

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