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Projections and embeddings of locally convex operator spaces and their duals

Published online by Cambridge University Press:  24 October 2008

Jan H. Fourie
Potchefstroom University, Potchefstroom 2520, South Africa
William H. Ruckle
Clemson University, Clemson, SC 29631, U.S.A.


Let E, F be Hausdorff locally convex spaces. In this note we consider conditions on E and F such that the dual space of the space Kb (E, F) (of quasi-compact operators) is a complemented subspace of the dual space of Lb (E, F) (of continuous linear operators). We obtain necessary and sufficient conditions for Lb(E, F) to be semi-reflexive.

Research Article
Copyright © Cambridge Philosophical Society 1984

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[1]Alfsen, E. M. and Effros, E. G.. Structure in real Banach spaces. Ann. of Math. (2) 96 (1972), 89173.Google Scholar
[2]Fleming, D. J. and Giarrusso, D. M.. Topological decompositions of the duals of locally convex operator spaces. Math. Proc. Cambridge Philos. Soc. 93 (1983), 307314.Google Scholar
[3]Hennefeld, J.. A decomposition for B(X*) and unique Hahn-Banach extensions. Pacific J. Math. 46 (1973), 197199.Google Scholar
[4]Holmes, R., Scranton, B. and Ward, J.. Approximation from the space of compact operators and other M-ideals. Duke Math. J. 42 (1979), 259269.Google Scholar
[5]Johnson, J.. Remarks on Banach spaces of compact operators. J. Funct. Anal. 32 (1979), 304311.Google Scholar
[6]Mach, J. and Ward, J. D.. Approximation by compact operators on certain Banach spaces. J. Approx. Theory 33 (1978), 274286.Google Scholar
[7]Saatkamp, K.. M-ideals of compact operators. Math. Z. 158 (1978), 253263.Google Scholar