Toeplitz Operators, $$\mathbb {T}^m$$-Invariance and Quasi-homogeneous Symbols

Quiroga-Barranco, Raul

doi:10.1007/s00020-021-02673-1

Cited by 2 publications

(5 citation statements)

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“…Finally, as was shown in [25], the most general form of these kind of symbols is given by adjoining a quasi-radial dependence to (3.11). That is, symbols of the form…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 98%

“…The next ingredient to the construction of the algebras we are studying is a family of Toeplitz operators whose symbols are subordinated to the aforementioned group [25]).…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

“…As an immediate consequence of the decomposition (3.13), the operator T φ j commutes with all operators from the C * algebra T k-qr . Moreover, summarizing the results from [25], the action of T φ j is given by the following proposition. Proposition 3.3 [25,Corollary 7.7] Let j ∈ {1, .…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

“…Moreover, summarizing the results from [25], the action of T φ j is given by the following proposition. Proposition 3.3 [25,Corollary 7.7] Let j ∈ {1, . .…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

“…, m} the operators T φ j 1 and T φ j 2 , acting on different "positions" with respect to the tensor product, commute. (See Section 7 from [25] for more details).…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

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.

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“…Finally, as was shown in [25], the most general form of these kind of symbols is given by adjoining a quasi-radial dependence to (3.11). That is, symbols of the form…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 98%

“…The next ingredient to the construction of the algebras we are studying is a family of Toeplitz operators whose symbols are subordinated to the aforementioned group [25]).…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

“…Moreover, summarizing the results from [25], the action of T φ j is given by the following proposition. Proposition 3.3 [25,Corollary 7.7] Let j ∈ {1, . .…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

“…, m} the operators T φ j 1 and T φ j 2 , acting on different "positions" with respect to the tensor product, commute. (See Section 7 from [25] for more details).…”

Section: Quasi-and Pseudo-homogeneous Symbolsmentioning

confidence: 99%

See 3 more Smart Citations