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

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 [25] in the case p = 2, which was proven by different methods. Further, we prove that every Toeplitz algebra which has a translation invariant C* subalgebra of the bounded uniformly continuous functions as its set of symbols is linearly generated by Toeplitz operators with the same space of symbols. (C) 2020 Elsevier Inc. All rights reserved.