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On homomorphisms between $C^{}$ -algebras and linear derivations on $C^{}$ -algebras

Chun-Gil Park; Hahng-Yun Chu; Won-Gil Park; Hee-Jeong Wee — 2005

Czechoslovak Mathematical Journal

It is shown that every almost linear Pexider mappings $f$ , $g$ , $h$ from a unital $C^{*}$ -algebra $𝒜$ into a unital $C^{*}$ -algebra $ℬ$ are homomorphisms when $f (2^{n} u y) = f (2^{n} u) f (y)$ , $g (2^{n} u y) = g (2^{n} u) g (y)$ and $h (2^{n} u y) = h (2^{n} u) h (y)$ hold for all unitaries $u \in 𝒜$ , all $y \in 𝒜$ , and all $n \in ℤ$ , and that every almost linear continuous Pexider mappings $f$ , $g$ , $h$ from a unital $C^{*}$ -algebra $𝒜$ of real rank zero into a unital $C^{*}$ -algebra $ℬ$ are homomorphisms when $f (2^{n} u y) = f (2^{n} u) f (y)$ , $g (2^{n} u y) = g (2^{n} u) g (y)$ and $h (2^{n} u y) = h (2^{n} u) h (y)$ hold for all $u \in {v \in 𝒜 ∣ v = v^{*} and v is invertible}$ , all $y \in 𝒜$ and all $n \in ℤ$ . Furthermore, we prove the Cauchy-Rassias stability of $*$ -homomorphisms between unital $C^{*}$ -algebras, and $ℂ$ -linear...

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Currently displaying 1 – 9 of 9

On homomorphisms between $C^{}$ -algebras and linear derivations on $C^{}$ -algebras

Stability of a 2-dimensional functional equation in a class of vector variable functions.

Stability of a Cauchy-Jensen functional equation in quasi-Banach spaces.

Approximate behavior of bi-quadratic mappings in quasinormed spaces.

On a cubic equation and a Jensen-quadratic equation.

A multidimensional functional equation having quadratic forms as solutions.

A functional equation originating from elliptic curves.

Partitioned cyclic functional equations.

Functional equations related to inner product spaces.