On derivations and elementary operators on C*- algebras (CROSBI ID 193625)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Gogić, Ilja
engleski
On derivations and elementary operators on C*- algebras
Let A be a unital C*-algebra with the canonical (H) C*-bundle B over the maximal ideal space of the centre of A, and let E(A) be the set of all elementary operators on A. We consider derivations on A which lie in the completely bounded norm closure of E(A), and show that such derivations are necessarily inner in the case when each fibre of B is a prime C*-algebra. We also consider separable C*-algebras A for which B is an (F) bundle. For these C*-algebras we show that the following conditions are equivalent: E(A) is closed in the operator norm ; A as a Banach module over its centre is topologically finitely generated ; fibres of B have uniformly finite dimensions, and each restriction bundle of B over a set where its fibres are of constant dimension is of finite type as a vector bundle.
C*-algebra ; derivation ; elementary operator ; ideal ; C*-bundle ; vector bundle
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Podaci o izdanju
56 (2)
2013.
515-534
objavljeno
0013-0915
1464-3839
10.1017/S0013091512000302