Toeplitz operators on the Hardy space with generalized pseudo-homogeneous symbols

Rodríguez, Miguel Ángel Rodríguez; Vasilevski, Nikolai

doi:10.1080/17476933.2021.1921757

Cited by 2 publications

(5 citation statements)

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“…It is natural to study the existence and structure of the above commutative Toeplitz algebras for different function Hilbert spaces such as the Hardy space over the unit sphere [24,30] or the Fock space of Gaussian square integrable entire functions [4,13]. In fact, there is an interesting interplay between these cases and the analysis of one of these spaces may be useful in the study of another.…”

Section: Communicated By Mihai Putinarmentioning

confidence: 99%

Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

Bauer,

Rodriguez Rodriguez

2023

Multivariable Operator Theory

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We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in C n . As an application we discuss semi-simplicity and the spectral invariance of these algebras. The different function Hilbert spaces are dealt with in parallel in successive chapters so that a direct comparison of the results is possible.As a new aspect of the theory we define commutative Toeplitz algebras over spaces of functions in infinitely many variables and present some structural results. The paper concludes with a short list of open problems in this area of research.Keywords Bergman and Hardy space • Gaussian measure in infinite dimensions • Fock space of functions in infinitely many variables • Commutative Banach algebras

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Section: Communicated By Mihai Putinarmentioning

confidence: 99%

Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

Bauer,

Rodriguez Rodriguez

2023

Multivariable Operator Theory

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“…It turns out that this condition suffices for much of the previous results to hold and so this was the approach in [30], where the so-called generalized pseudo-homogeneous symbols were introduced. These symbols are defined by…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

Section: Communicated By Mihai Putinarmentioning

confidence: 99%

“…Section 4 carries out the corresponding analysis in case of the classical Hardy space H 2 (S 2n−1 ) over the unit sphere S 2n−1 in C n , see [1,10,24,30]. An useful ingredient to the proofs is a decomposition of Toeplitz operators (with certain symbols) as an infinite sum of Bergman space Toeplitz operators over B n−1 with integer weights.…”

Section: Communicated By Mihai Putinarmentioning

confidence: 99%

“…is an operator on a finitedimensional space one has the following result. Lemma 3.6 (See [30,Section 3.3]). Let j ∈ {1, .…”

Section: Gelfand Theorymentioning

confidence: 99%

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Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

Bauer

Rodríguez

2022

Complex Anal. Oper. Theory

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We present a survey and new results on the construction and Gelfand theory of commutative Toeplitz algebras over the standard weighted Bergman and Hardy spaces over the unit ball in $$\mathbb {C}^n$$ C n . As an application we discuss semi-simplicity and the spectral invariance of these algebras. The different function Hilbert spaces are dealt with in parallel in successive chapters so that a direct comparison of the results is possible. As a new aspect of the theory we define commutative Toeplitz algebras over spaces of functions in infinitely many variables and present some structural results. The paper concludes with a short list of open problems in this area of research.

show abstract

Toeplitz operators on the Hardy space with generalized pseudo-homogeneous symbols

Cited by 2 publications

References 10 publications

Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

Commutative Toeplitz Algebras and Their Gelfand Theory: Old and New Results

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