Equivalence in Operator Algebras.

A Morita Type Equivalence for Dual Operator Algebras

We generalize the main theorem of Rieffel for Morita equivalence of W -algebras to the case of unital dual operator algebras: two unital dual operator algebras A,B have completely isometric normal representations α, β such that α(A) = [Mβ(B)M] ∗ and β(B) = [Mα(A)M] ∗ for a ternary ring of operators M (i.e. a linear space M such that MMM ⊂ M) if and only if there exists an equivalence functor F ...

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