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Journal of Operator Theory

Volume 73, Issue 2, Spring 2015  pp. 281-314.

Compactness and essential norm properties of operators on generalized Fock spaces

Authors:  Joshua Isralowitz
Author institution:Department of Mathematics and Statistics, SUNY Albany, Albany, NY, 12222, U.S.A.

Summary: The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient conditions for a wide class of operators (which includes operators in the Toeplitz algebra generated by bounded symbols) to be compact and we obtain related estimates on the essential norm of such operators. Finally, we discuss interesting open problems related to our results.

Keywords: Toeplitz operators, generalized Fock spaces, essential norm, compactness, Berezin transform

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