A Z* algebra is a C^* algebra whose all positive elements are zero divisor.
The family of all Z^* algebras with C^* morphisms forms a category.
Is the category of Z^* algebras equivalent to the category of C^* algebras?
If the answer would be positive then the theory of C* algebras can be reduced to study of Z^* algebras
The equivalence of two categories is meant in the following sense: