Centralizers in semisimple algebras, and descent spectrum in Banach algebras

Projective Spectrum in Banach Algebras

For a tuple A = (A0, A1, ..., An) of elements in a unital Banach algebra B, its projective spectrum p(A) is defined to be the collection of z = [z0, z1, ..., zn] ∈ P such that A(z) = z0A0 + z1A1 + · · · + znAn is not invertible in B. The pre-image of p(A) in Cn+1 is denoted by P (A). When B is the k × k matrix algebra Mk(C), the projective spectrum is a projective hypersurface. In infinite dime...

Spectrum Preserving Linear Maps Between Banach Algebras

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

σ-Derivations in Banach algebras

Derivations in semiprime rings and Banach algebras

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,yin R$ where $0neq bin R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. ...