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A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B+A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$. A point $G$ in $\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.
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참고문헌 (20)
참고문헌 신청
A. Essaleh / / Weak-local derivations and homomorphisms on C*-algebras / arxiv:1411.4795
F. Gilfeather / 1986 / Isomorphisms of certain CSL algebras / J. Func. Anal 67 (2) : 264 ~ 291
F. Lu / 2006 / Lie derivations of certain CSL algebras / Israel J. Math 155 : 149 ~ 156
F. Lu / 2009 / Characterizations of derivations and Jordan derivations on Banach algebras / Linear Algebra Appl 430 (8-9) : 2233 ~ 2239
G. An / 2016 / Characterizations of linear mappings through zero products or zero Jordan products / Electron. J. Linear Algebra 31 : 408 ~ 424
F. Gilfeather / 1986 / Isomorphisms of certain CSL algebras / J. Func. Anal 67 (2) : 264 ~ 291
F. Lu / 2006 / Lie derivations of certain CSL algebras / Israel J. Math 155 : 149 ~ 156
F. Lu / 2009 / Characterizations of derivations and Jordan derivations on Banach algebras / Linear Algebra Appl 430 (8-9) : 2233 ~ 2239
G. An / 2016 / Characterizations of linear mappings through zero products or zero Jordan products / Electron. J. Linear Algebra 31 : 408 ~ 424
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