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ArticleOriginal scientific text

Title

Operators preserving ideals in C*-algebras

Authors 1

Affiliations

  1. Department of Mathematics, Vologda Polytechnical Institute, 15 Lenin St., 160008 Vologda, Russia

Abstract

The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.

Keywords

ENG
C*-algebra, derivation, reflexivity

Bibliography

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  3. J. W. Bunce and W. L. Paschke, Derivations on a C*-algebra and its dual, ibid. 37 (1980), 235-247.
  4. U. Haagerup, All nuclear C*-algebras are amenable, Invent. Math. 74 (1983), 305-319.
  5. R. Kadison, Local derivations, J. Algebra 130 (1990), 494-509.
  6. J. Kraus and D. R. Larson, Reflexivity and distance formulae, Proc. London Math. Soc. 53 (1986), 340-356.
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Studia Mathematica
1994/109/1
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Pages:
67-72
Main language of publication
English
Received
1993-04-27
Accepted
1993-09-19
Published
1994
Exact and natural sciences