Transcendental quasi-nilpotents in operator algebras

Expanding Quasi-MV Algebras by a Quantum Operator

We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety p 0QMV of such p 0 quasi-MV algebras has a subquasivariety whose members called cartesian can be obtained in an appropriate way out of MV algebras. After showing that cartesian p 0 quasi-MV algebras generate p 0QMV, we prove a standard completeness theorem for p 0QMV w.r.t. an algebra over t...

Operator Algebras

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

Operator Theory and Operator Algebras

Orientation in operator algebras.

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

Multiplicative bijective maps on standard operator algebras