Communications in Mathematical Analysis

Quasi-radial Operators on the Weighted Bergman Space over the Unit Ball

A. Garcia and N. Vasilevski

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Abstract

We study the so-called quasi-radial operators, i.e., the operators that are invariant under the subgroup of the unitary group ${\mathfrak U}(n)$ formed by the block-diagonal matrices with unitary blocks of fixed dimensions. The quasi-radial Toeplitz operators appear naturally and play a crucial role under the study of the commutative Banach (not $C^*$) algebras of Toeplitz operators [1, 8]. They form an intermediate class of operators between the Toeplitz operators with radial $a=a(r)$, $r=\sqrt{|z_1|^2 + \ldots + |z_n|^2}$, and separately-radial $a = a(|z_1|, \ldots, |z_n|)$ symbols.

Article information

Source
Commun. Math. Anal., Volume 17, Number 2 (2014), 178-188.

Dates
First available in Project Euclid: 18 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.cma/1418919763

Mathematical Reviews number (MathSciNet)
MR3292967

Zentralblatt MATH identifier
1334.47032

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Keywords
Banach algebra Berezin transform Toeplitz operator quasi-radial operator quasi-radialization

Citation

Garcia, A.; Vasilevski, N. Quasi-radial Operators on the Weighted Bergman Space over the Unit Ball. Commun. Math. Anal. 17 (2014), no. 2, 178--188. https://projecteuclid.org/euclid.cma/1418919763


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