Displaying similar documents to “Some Results about the Spectrum of Commutative Banach Algebras under the Weak Topology and Applications.”

A generalization of peripherally-multiplicative surjections between standard operator algebras

Takeshi Miura, Dai Honma (2009)

Open Mathematics

Similarity:

Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B...

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici

Similarity:

We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

On generalized derivations in Banach algebras

Nadia Boudi, Said Ouchrif (2009)

Studia Mathematica

Similarity:

We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.