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Compactness of operators on generalized Fock spaces (1212.5994v2)
Published 25 Dec 2012 in math.FA and math.CV
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.