Factorization in Operator Algebras

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.

Factorization in the Composition Algebras

Let O be a maximal arithmetic in one of the four (non-split) composition algebras over R, and let ] = mn be the norm of an element in O. Rehm 15] describes an algorithm for nding all factorizations of as = , where ] = m, ] = n and (m; n) = 1. Here, we extend the algorithm to general , m, and n, providing precise geometrical conngurations for the sets of left-and right-hand divisors.

Multiplicative bijective maps on standard operator algebras