We shall present in this paper the results on
recognition of equivalences in the shape
category of arbitrary
\gt {C^{\star}}{algebras} described recently
by the author. These results resemble
analogous G. Kozlowski's characterization of
shape equivalences in the usual (commutative)
shape theory. As an application, we give also
some characterizations of
\gt {C^{\star}}{algebras} of trivial shape.