Some remarks on derivations on the algebra of operators in Hilbert pro-C*-bimodules

Autor:	Karimi, Khadijeh, Sharifi, Kamran
Rok vydání:	2016
Předmět:	Mathematics - Operator Algebras Primary 46L08 Secondary 46L05 46H25 47B47
Druh dokumentu:	Working Paper
Popis:	Suppose $A$ is a pro-C*-algebra. Let $L_{A}(E)$ be the pro-C*-algebra of adjointable operators on a Hilbert $A$-module $E$ and let $K_{A}(E)$ be the closed two sided $*$-ideal of all compact operators on $E$. We prove that if $E$ be a full Hilbert $A$-module, the innerness of derivations on $K_{A}(E)$ implies the innerness of derivations on $L_{A}(E)$. We show that if $A$ is a commutative pro-C*-algebra and $E$ is a Hilbert $A$-bimodule then every derivation on $K_{A}(E)$ is zero. Moreover, if $A$ is a commutative $\sigma$-C*-algebra and $E$ is a Hilbert $A$-bimodule then every derivation on $L_{A}(E)$ is zero, too. Comment: 8 pages, accepted
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.03282 Zobrazit plný text záznamu View this record from Arxiv