# Operators preserving ideals in C*-algebras

Studia Mathematica (1994)

- Volume: 109, Issue: 1, page 67-72
- ISSN: 0039-3223

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topShul'Man, V.. "Operators preserving ideals in C*-algebras." Studia Mathematica 109.1 (1994): 67-72. <http://eudml.org/doc/216061>.

@article{ShulMan1994,

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.},

author = {Shul'Man, V.},

journal = {Studia Mathematica},

keywords = {C*-algebra; derivation; reflexivity; derivations of a -algebra; derivations in -algebras},

language = {eng},

number = {1},

pages = {67-72},

title = {Operators preserving ideals in C*-algebras},

url = {http://eudml.org/doc/216061},

volume = {109},

year = {1994},

}

TY - JOUR

AU - Shul'Man, V.

TI - Operators preserving ideals in C*-algebras

JO - Studia Mathematica

PY - 1994

VL - 109

IS - 1

SP - 67

EP - 72

AB - 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.

LA - eng

KW - C*-algebra; derivation; reflexivity; derivations of a -algebra; derivations in -algebras

UR - http://eudml.org/doc/216061

ER -

## References

top- [1] C. A. Akemann, The general Stone-Weierstrass problem, J. Funct. Anal. 4 (1969), 277-294. Zbl0177.17603
- [2] W. Arveson, Interpolation problems in nest algebras, ibid. 20 (1975), 208-233. Zbl0309.46053
- [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. Zbl0529.46041
- [5] R. Kadison, Local derivations, J. Algebra 130 (1990), 494-509. Zbl0751.46041
- [6] J. Kraus and D. R. Larson, Reflexivity and distance formulae, Proc. London Math. Soc. 53 (1986), 340-356. Zbl0623.47046
- [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). Zbl0327.46073
- [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).

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