Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

Bauer, Wolfram; Yañez, Crispin Herrera; Vasilevski, Nikolai

doi:10.1007/s00020-013-2101-1

Cited by 28 publications

(21 citation statements)

References 10 publications

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“…The results of Suárez have been complemented and generalized to the weighted Bergman space on the unit ball in [1,2,10,15]. The above ∞ -closure of d 1 was characterized in [10].…”

Section: Introductionmentioning

confidence: 99%

C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

Esmeral

Maximenko

Vasilevski

2015

Integr. Equ. Oper. Theory

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We consider the set of all Toeplitz operators acting on the weighted Bergman space over the upper half-plane whose L∞-symbols depend only on the argument of the polar coordinates. The main result states that the uniform closure of this set coincides with the C * -algebra generated by the above Toeplitz operators and is isometrically isomorphic to the C * -algebra of bounded functions that are very slowly oscillating on the real line in the sense that they are uniformly continuous with respect to the arcsinh-metric on the real line.Mathematics Subject Classification. Primary: 47B35; Secondary: 32A36.

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“…The results of Suárez have been complemented and generalized to the weighted Bergman space on the unit ball in [1,2,10,15]. The above ∞ -closure of d 1 was characterized in [10].…”

Section: Introductionmentioning

confidence: 99%

C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

Esmeral

Maximenko

Vasilevski

2015

Integr. Equ. Oper. Theory

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“…It is an interesting question, which sequences of numbers γ γ γ may serve as the spectral sequence of an operator T a , with certain symbol a(r) ∈ L 1 (R + ). For a similar problem for radial Toeplitz operators in the Bergman space on the disk, such complete description has been found in [8].…”

Section: Radial Toeplitz Operatorsmentioning

confidence: 86%

Toeplitz Operators in the Herglotz Space

Rozenblioum

Vasilevski

2016

Integr. Equ. Oper. Theory

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Abstract. We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in R d . As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach based upon the reproducing kernel nature of the Herglotz space and sesquilinear forms, which results in a meaningful theory. For two important patterns of sesquilinear forms we discuss a number of properties, including the uniqueness of determining the symbols from the operator, the finite rank property, the conditions for boundedness and compactness, spectral properties, certain algebraic relations.

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“…Recall [5,Section 5] that the sequence , of a Toeplitz operator belongs to the * -algebra SO(Z + ), where SO(Z + ) consists of all bounded sequences that slowly oscillate in the sense of Schmidt [6]; that is,…”

Section: Toeplitz Operators With Radial Symbols Given a Sequencementioning

confidence: 99%

“…Moreover [5,Section 5], the * -algebra T rad is isomorphic and isometric to the algebra SO(Z + ), via identification of a diagonal operator with its eigenvalue sequence.…”

Section: Toeplitz Operators With Radial Symbols Given a Sequencementioning

confidence: 99%

Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

García

Vasilevski²

2015

Journal of Function Spaces

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We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory.

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Eigenvalue Characterization of Radial Operators on Weighted Bergman Spaces Over the Unit Ball

Cited by 28 publications

References 10 publications

C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

Toeplitz Operators in the Herglotz Space

Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball

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