Weakly Compact Homomorphisms from Group Algebras

Compact Homomorphisms of (t-algebras

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

Weakly Compact #?-algebras

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

Module homomorphisms from Frechet algebras

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

Norm Decreasing Homomorphisms of Group Algebras

Homomorphisms and Idempotents of Group Algebras

where (x, g) denotes % evaluated at g. Each % thus yields a homomorphism of M(G) onto the complex numbers. Every such homomorphism of L(G) is obtained in this way. Let be a homomorphism of L{G) into M(H). After composing with <[>, every homomorphism of M(H) onto the complex numbers either is identically zero, or can be identified with a member of G. We thus have a map <£* from Ê into {G, 0 ...