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 [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.