Spatiality of Derivations of Operator Algebras in Banach Spaces

Quanyuan Chen and Xiaochun Fang

Abstract and Applied Analysis, 2011, vol. 2011, 1-13

Abstract:

Suppose that is a transitive subalgebra of and its norm closure contains a nonzero minimal left ideal . It is shown that if is a bounded reflexive transitive derivation from into , then is spatial and implemented uniquely; that is, there exists such that for each , and the implementation of is unique only up to an additive constant. This extends a result of E. Kissin that “if contains the ideal of all compact operators in , then a bounded reflexive transitive derivation from into is spatial and implemented uniquely.” in an algebraic direction and provides an alternative proof of it. It is also shown that a bounded reflexive transitive derivation from into is spatial and implemented uniquely, if is a reflexive Banach space and contains a nonzero minimal right ideal .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:813723

DOI: 10.1155/2011/813723

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