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arXiv · 1911.12668

Correspondence theory on $p$-Fock spaces with applications to Toeplitz algebras

Robert Fulsche
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Abstract

We prove several results concerning the theory of Toeplitz algebras over $p$-Fock spaces using a correspondence theory of translation invariant symbol and operator spaces. The most notable results are: The full Toeplitz algebra is the norm closure of all Toeplitz operators with bounded uniformly continuous symbols. This generalizes a result obtained by J. Xia (J. Funct. Anal. 269:781-814, 2015) in the case $p = 2$, which was proven by different methods. Further, we prove that every Toeplitz algebra which has a translation invariant $C^\ast$ subalgebra of the bounded uniformly continuous functions as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols.

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Robert Fulsche. 2020-06-02. Correspondence theory on $p$-Fock spaces with applications to Toeplitz algebras. https://doi.org/10.1016/j.jfa.2020.108661

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