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2014 Quasi-radial Operators on the Weighted Bergman Space over the Unit Ball
A. Garcia, N. Vasilevski
Commun. Math. Anal. 17(2): 178-188 (2014).


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.


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A. Garcia. N. Vasilevski. "Quasi-radial Operators on the Weighted Bergman Space over the Unit Ball." Commun. Math. Anal. 17 (2) 178 - 188, 2014.


Published: 2014
First available in Project Euclid: 18 December 2014

zbMATH: 1334.47032
MathSciNet: MR3292967

Primary: 47B35

Keywords: Banach Algebra , ‎Berezin transform , quasi-radial operator , quasi-radialization , Toeplitz operator

Rights: Copyright © 2014 Mathematical Research Publishers

Vol.17 • No. 2 • 2014
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