科研之友
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摘要
Let N be a nest on a real or complex Banach space X and let AlgN be the associated nest algebra. Omega is an element of AlgN is called an additively all-derivable point if for any additive map delta : AlgN -> AlgN, delta(AB) = delta(A)B + A delta(B) holds for any A, B is an element of AlgN with AB = Omega implies that delta is an additive derivation. Assume that P is an idempotent operator with range ran(P) = N-0 for some nontrivial N-0 is an element of N. Let Omega is an element of AlgN be any operator satisfying that P Omega P = Omega (or (l - P)Omega(l - P) = Omega). We show that, if Omega vertical bar(ran(P)) (or Omega vertical bar(ran(l - P))) is injective or has dense range, then Omega is an additively all-derivable point. Moreover, if X is infinite dimensional, then every additive map derivable at such an Omega is an inner derivation.
- 出版日期2012-9
- 单位太原理工大学
