IRREDUCIBLE OPERATOR ALGEBRAS

Irreducible Representations of Operator Algebras

Irreducible Positive Linear Maps on Operator Algebras

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible...

Subdirectly irreducible separable dynamic algebras

A characterization of the subdirectly irreducible separable dynamic algebras is presented. The notions developed for this study were also suitable to describe the previously found class of the simple separable dynamic algebras.

Subdirectly Irreducible Quasi-modal Algebras

In this paper we give suitable notions of congruences and subdirectly irreducible algebras for the class of quasi-modal algebras introduced in [1]. We also prove some characterizations of subdirectly irreducible algebras following the similar results given by G. Sambin [5] for modal 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, ...