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

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.

34 pages; Minor changes according to the suggestions of the anonymous reviewer

References in corpus (2)

• Fredholmness of Toeplitz operators on the Fock space
• Algebras of Toeplitz operators on the $n$-dimensional unit ball

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