Isomorphisms of abelian group 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...

Warfield invariants in Abelian group algebras

LetF be a field of characteristic p 6= 0 andG an Abelian group. For each prime q and each ordinal α we calculate in terms of G and its sections the Warfield q-invariantsWα,q(V (FG)) of the group V (FG) of all normalized units in the commutative group algebra FG when either q = p,Gt/Gp is infinite and F is perfect, orG is p-mixed. Surprisingly, these invariants do not depend on F . This supplies...

Isometric Isomorphisms of Measure Algebras

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...

Commutative group algebras of highly torsion-complete abelian p-groups

A new class of abelian p-groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).