  We define co-Toeplitz operators, a new class of Hilbert space operators, in
order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz
quantization scheme introduced by the author in the setting of symbols that
come from a possibly non-commutative algebra with unit. In the present dual
setting the symbols come from a possibly non-co-commutative co-algebra with
co-unit. However, this co-Toeplitz quantization is a usual quantization scheme
in the sense that to each symbol we assign a densely defined linear operator
acting in a fixed Hilbert space. Creation and annihilation operators are also
introduced as certain types of co-Toeplitz operators, and then their
commutation relations provide the way for introducing Planck's constant into
this theory. The domain of the co-Toeplitz quantization is then extended as
well to a set of co-symbols, which are the linear functionals defined on the
co-algebra. A detailed example based on the quantum group (and hence
co-algebra) $SU_q(2)$ as symbol space is presented.
