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Some algebraic properties of F(X) and K(X)

Published online by Cambridge University Press:  20 January 2009

Freda E. Alexander
Freda E. Alexander
Affiliation:
University of Glasgow, Glasgow G12 8WQ
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Throughout we consider operators on a reflexive Banach space X. We consider certain algebraic properties of F(X), K(X) and B(X) with the general aim of examining their dependence on the possession by X of the approximation property. B(X) (resp. K(X)) denotes the algebra of all bounded (resp. compact) operators on X and F(X) denotes the closure in B(X) of its finite rank operators. The two questions we consider are:

(1) Is K(X) equal to the set of all operators in B(X) whose right and left multiplication operators on F(X) (or on B(X)) are weakly compact?

(2) Is F(X) a dual algebra?

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 4 , September 1975 , pp. 353 - 361
Copyright
Copyright © Edinburgh Mathematical Society 1975

References

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