Norm decreasing homomorphisms between group algebras

Norm Decreasing Homomorphisms of Group Algebras

Homomorphisms of Group Algebras with Norm Less than V2

We show that two locally compact abelian groups Gx and G2 are isomorphic if there exists an algebra isomorphism T of L\Gλ) onto L\G2) with | | Γ | | < V2. This constant is best possible. The same result is proved for locally compact connected groups, but for the general locally compact group, the result is proved under the hypothesis | |T | |< 1.246. Similar results are given for the algebras C...

Homomorphisms between Solomon's Descent Algebras

In a previous paper (see Garsia-Reutenauer [2]), we have studied algebraic properties of the descent algebras Σ n , and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of Poincaré-Birkhoff-Witt's theorem. In the present paper, we study homomorphisms between these algebras Σ n. The existence of these homomorphisms was suggested by pro...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet 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 ...