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Elementary operators on prime C*-algebras II†
Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 275-284

Voir la notice de l'article provenant de la source Cambridge University Press

Compact elementary operators acting on the algebra L(H) of all bounded operators on some Hilbert space H were characterised by Fong and Sourour in [9]. Akemann and Wright investigated compact and weakly compact derivations on C*-algebras [1], and also studied compactness properties of the sum and the product of the right and the left regular representation of an element in a C*-algebra [2]. They used the concept of a compact Banach algebra element due to Vala [17]: an element a in a Banach algebra A is called compact if the mapping x → axa is compact on A. This notion has been further investigated by Ylinen [18, 19, 20], who showed in particular that a is a compact element of the C*-algebra A if x ↦ axa is weakly compact on A [19]. 
Mathieu, Martin. Elementary operators on prime C*-algebras II†. Glasgow mathematical journal, Tome 30 (1988) no. 3, pp. 275-284. doi: 10.1017/S0017089500007369
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