Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

5-2018

Originally Published In

Journal of Mathematical Analysis and Applications Volume 461, Issue 2, 15 May 2018, Pages 1711-1732. https://doi.org/10.1016/j.jmaa.2017.12.046

Abstract

For 0<p≤∞, let F be the Fock space induced by a weight function φ satisfying ddcφω0. In this paper, given p∈(0,1] we introduce the concept of weakly localized operators on F, we characterize the compact operators in the algebra generated by weakly localized operators. As an application, for 0<p<∞ we prove that an operator T in the algebra generated by bounded Toeplitz operators with BMO symbols is compact on F if and only if its Berezin transform satisfies certain vanishing property at ∞. In the classical Fock space, we extend the Axler-Zheng condition on linear operators T, which ensures T is compact on F for all possible 0<p<∞.

Comments

Preprint version of article published in Journal of Mathematical Analysis and Applications Volume 461, Issue 2, 15 May 2018, Pages 1711-1732. https://doi.org/10.1016/j.jmaa.2017.12.046. © 2017 Elsevier Inc.

DOI

10.1016/j.jmaa.2017.12.046

Previous Versions

Feb 21 2018

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