Isomorphisms of Diagonalizable Algebras

Isomorphisms in unital $C^*$-algebras

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

Diagonalizable Derivations of Finite-dimensional Algebras Ii

When an algebra is graded by a group, any additive character of the group induces a diagonalizable derivation of the ring. This construction is studied in detail for the case of a path algebra modulo relations and its fundamental group. We describe an injection of the character group into the first cohomology group following Assem-de la Peña. Rather general conditions are determined, in this co...

Isometric Isomorphisms of Measure Algebras

A Representation Theorem for Co-diagonalizable Algebras

This abstract is a summary of a lecture given at the Seminar of the Department of Logic and Methodology of Sciences, Wroc law University, 23 May 1985. The present work refers directly to the investigations of Buszkowski and Prucnal [1] and that of Esakia [2], generalizing their results. Our main representation theorem for co-diagonalizable algebras (Theorem 2) is obtained by application of cert...

Isomorphisms between Topological Conjugacy Algebras

A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that ηi : Xi → Xi is a continuous proper map on a locally compact Hausdorff space Xi, for i = 1, 2. We show that the dynamical systems (X1, η1) and (X2, η2) are conjugate if and only if some topological conjugacy algebra of (X1, η1) is is...