Compactness of operators on generalized Fock spaces

Joshua Isralowitz

Compactness of operators on generalized Fock spaces

Functional Analysis 2013-06-04 v2 Complex Variables

Authors: Joshua Isralowitz

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.

Keywords

generalized Fock spaces Toeplitz operators compact operators measure symbol norm closure Hilbert space

Cite

@article{arxiv.1212.5994,
  title  = {Compactness of operators on generalized Fock spaces},
  author = {Joshua Isralowitz},
  journal= {arXiv preprint arXiv:1212.5994},
  year   = {2013}
}

Comments

This paper has been withdrawn since the results in this paper are vastly generalized by those in http://arxiv.org/abs/1305.7475

Compactness of operators on generalized Fock spaces

Abstract

Keywords

Cite

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