  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.
