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Spatiality of Derivations of Operator Algebras in Banach Spaces

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  • Quanyuan Chen
  • Xiaochun Fang

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 .

Suggested Citation

  • Quanyuan Chen & Xiaochun Fang, 2011. "Spatiality of Derivations of Operator Algebras in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-13, November.
    • Handle: RePEc:hin:jnlaaa:813723
    DOI: 10.1155/2011/813723
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