Characterization of ($α$,$α$)-derivation on $B(X)$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909138975457280 |
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| author | Chen, Quanyuan Li, Yaqi |
| author_facet | Chen, Quanyuan Li, Yaqi |
| contents | Let $X$ be a Banach algebra and $B(X)$ be the set of all bounded linear operators on $X$. Suppose that $α: B(X) \rightarrow B(X)$ is an automorphism. We say that a mapping $δ$ from $B(X)$ into itself is derivable at $G \in B(X)$ if $δ(G) = α(A)δ(B) + δ(A)α(B)$ for all $A, B \in B(X)$ with $AB = G$. We say that an element $G \in B(X)$ is an $(α,α)$-all derivable point of $B(X)$ if every $(α,α)$-derivable mapping $δ$ at G is an $(α,α)$-derivation. In this paper, we show that every $(α,α)$-derivable mapping at a nonzero element in $B(X)$ is an $(α,α)$-derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterization of ($α$,$α$)-derivation on $B(X)$ Chen, Quanyuan Li, Yaqi Functional Analysis Operator Algebras Let $X$ be a Banach algebra and $B(X)$ be the set of all bounded linear operators on $X$. Suppose that $α: B(X) \rightarrow B(X)$ is an automorphism. We say that a mapping $δ$ from $B(X)$ into itself is derivable at $G \in B(X)$ if $δ(G) = α(A)δ(B) + δ(A)α(B)$ for all $A, B \in B(X)$ with $AB = G$. We say that an element $G \in B(X)$ is an $(α,α)$-all derivable point of $B(X)$ if every $(α,α)$-derivable mapping $δ$ at G is an $(α,α)$-derivation. In this paper, we show that every $(α,α)$-derivable mapping at a nonzero element in $B(X)$ is an $(α,α)$-derivation. |
| title | Characterization of ($α$,$α$)-derivation on $B(X)$ |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2403.02815 |