Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach

Rozenblum, Grigori; Vasilevski, Nikolai

doi:10.1007/s00020-022-02706-3

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Gelfand Theory For1

Introduction1

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2023

2024

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Cited by 4 publications

(2 citation statements)

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“…Remark 2. Since the Gelfand transform of polynomials of W w (1,0) and W w (0,1) generates all polynomials on T 2 , we obtain a result in the spirit of the work [20]: The C * algebra C 1 ∩ A G is obtained as…”

Section: Gelfand Theory Formentioning

confidence: 79%

Correspondence theory on p-Fock spaces with applications to Toeplitz algebras

Robert

2020

Journal of Functional Analysis

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Section: Gelfand Theory Formentioning

confidence: 79%

Correspondence theory on p-Fock spaces with applications to Toeplitz algebras

Robert

2020

Journal of Functional Analysis

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“…Nevertheless, the problem of describing the commutant of a given Toeplitz operator, i.e., the set of all Toeplitz operators that commute (in a sense of composition) with it, is still far from being totally solved. Almost nothing is known to us about when T f T g = T g T f for "general symbols" f and g. See [1,2,3,4,6,7,9,10,12,14,15] to know more about the commuting problem of Toeplitz operators on L 2 a (D) and the answers obtained so far for certain classes of symbols.…”

Section: Introductionmentioning

confidence: 99%

On the powers of quasihomogeneous Toeplitz operators

Bouhali¹,

Bendaoud²,

Louhichi³

2021

Czech.Math.J.

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A major open question in the theory of Toeplitz operator on the Bergman space of the unit disk of the complex plane is to fully characterize the set of all Toeplitz operators that commute with a given one. In [2], the second author described the sum S = T e imθ f +T e ilθ g , where f and g are radial functions, that commutes with the sum T = T e ipθ r (2M +1)p + T e isθ r (2N +1)s . It is proved that S = cT , where c is a constant. In this article, we shall replace r (2M +1)p and r (2N+1)s by r n and r d respectively, with n and d in N, and we shall show that the same result holds.

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Spectral theorem approach to commutative C⁎-algebras generated by Toeplitz operators on the unit ball: Quasi-elliptic related cases

Rozenblum

Vasilevski

2023

Journal of Mathematical Analysis and Applications

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Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach

Cited by 4 publications

References 12 publications

Correspondence theory on p-Fock spaces with applications to Toeplitz algebras

Correspondence theory on p-Fock spaces with applications to Toeplitz algebras

On the powers of quasihomogeneous Toeplitz operators

Spectral theorem approach to commutative C⁎-algebras generated by Toeplitz operators on the unit ball: Quasi-elliptic related cases

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