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arXiv · 1212.5994

Compactness of operators on generalized Fock spaces

Joshua Isralowitz
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Abstract

For a very general class of weighted Fock spaces on $\mathbb{C}^n$, we give necessary and sufficient conditions for a Toeplitz operator with a (not necessarily positive) measure symbol to be compact. Furthermore, we show that all compact operators are in the norm closure of the algebra generated by Toeplitz operators with $C_c ^\infty(\mathbb{C}^n)$ symbols, and in the Hilbert space setting show that all compact operators are in the norm closure of the set of such Toeplitz operators.

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Joshua Isralowitz. 2013-06-03. Compactness of operators on generalized Fock spaces. https://arxiv.org/abs/1212.5994

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