Ring homomorphisms on real Banach algebras.
Real-linear isometries between function algebras
Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily...
A note on a class of Banach algebra-valued polynomials.
Superstability of generalized multiplicative functionals.
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras.
Superstability of multipliers and ring derivations on Banach algebras.
A reconsideration of Hua's inequality. II.
Stability of multipliers on Banach algebras.
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
A reconsideration of Hua's inequality.
Continuously differentiable means.
A generalization of peripherally-multiplicative surjections between standard operator algebras
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 −1 for some...
Real linear isometries between function algebras. II
We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.
Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras
Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M A and M B, respectively, and let r(a) be the spectral radius of a. We show that if T: A → B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b ∈ A, then there exist a homeomorphism φ: M B → M A and a closed and open subset K of M B such that for all a ∈ A, where e is unit element of A. If, in addition, and on M B, then T is an algebra isomorphism.
Page 1