Naslov
On derivations and elementary operators on C*- algebras

Autori
Gogić, Ilja

Izvornik
Proceedings of the edinburgh mathematical society (0013-0915) 56 (2013), 2; 515-534

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
C*-algebra ; derivation ; elementary operator ; ideal ; C*-bundle ; vector bundle

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA