Derivations on Banach algebras of connected multiplicative linear functionals

Autor: M. J. Mehdipour, M. Ghasemi
Rok vydání: 2020
Předmět:
Zdroj: Bulletin of the Malaysian Mathematical Sciences Society. 44:1727-1748
ISSN: 2180-4206
0126-6705
DOI: 10.1007/s40840-020-01029-z
Popis: Let A and B be Banach algebras with $$\sigma (B)\ne \emptyset $$ . Let $$\theta , \phi , \gamma \in \sigma (B)$$ and $$\mathrm{Der}(A\times _\theta ^{\phi , \gamma }B)$$ be the set of all linear mappings $$d: A\times B\rightarrow A\times B$$ satisfying $$d((a, b)\cdot _\theta (x, y))=d(a, b)\cdot _\phi (x, y)+ (a, b)\cdot _\gamma d(x, y)$$ for all $$a, x\in A$$ and $$b, y\in B$$ . In this paper, we characterize elements of $$\mathrm{Der}(A\times _\theta ^{\phi , \gamma }B)$$ in the case where A has a right identity. We then investigate the concept of centralizing for elements of $$\mathrm{Der}(A\times _\theta ^{\phi , \gamma }B)$$ and determine dependent elements of $$\mathrm{Der}(A\times _\theta ^{\phi , \gamma }B)$$ . We also apply some results to group algebras.
Databáze: OpenAIRE
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