Operators preserving ideals in C*-algebras

• Autorzy: V. S. Shul'Man
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

C*-algebra; derivation; reflexivity

Kategorie tematyczne

• 47C15: Operators in C * - or von Neumann algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 1
• Strony: 67-72

Daty

wydano

1994

otrzymano

1993-04-27

poprawiono

1993-09-19

Twórcy

autor

V. S. Shul'Man

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

Bibliografia

• [1] C. A. Akemann, The general Stone-Weierstrass problem, J. Funct. Anal. 4 (1969), 277-294.
• [2] W. Arveson, Interpolation problems in nest algebras, ibid. 20 (1975), 208-233.
• [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.
• [7] A. J. Loginov and V. S. Shul'man, Hereditary and intermediate reflexivity of W*-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), 1260-1273 (in Russian).
• [8] V. S. Shul'man, On the geometry of some pairs of subspaces in C*-algebras, in: Spectral Theory of Operators and its Applications, No. 6, Elm, Baku, 1985, 196-216 (in Russian).