  This note is a follow-up to a recent paper by the author. Most of that theory
is now realized in a new setting where the vector space of symbols is not
necessarily an algebra nor is it equipped with an inner product, although it
does have a conjugation. As in the previous paper one does not need to put a
measure on this vector space. A Toeplitz quantization is defined and shown to
have most of the properties as in the previous paper, including creation and
annihilation operators. As in the previous paper this theory is implemented by
densely defined Toeplitz operators which act in a Hilbert space, where there is
an inner product, of course. Planck's constant also plays a role in the
canonical commutation relations of this theory.
