Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-18T08:26:42.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Projections and embeddings of locally convex operator spaces and their duals

Published online by Cambridge University Press:  24 October 2008

Jan H. Fourie  and
William H. Ruckle
Jan H. Fourie
Affiliation:
Potchefstroom University, Potchefstroom 2520, South Africa
William H. Ruckle
Affiliation:
Clemson University, Clemson, SC 29631, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 321 - 323
Copyright
Copyright © Cambridge Philosophical Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Alfsen, E. M. and Effros, E. G.. Structure in real Banach spaces. Ann. of Math. (2) 96 (1972), 89–173.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), 307–314.Google Scholar
[3]Hennefeld, J.. A decomposition for B(X*) and unique Hahn-Banach extensions. Pacific J. Math. 46 (1973), 197–199.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), 259–269.Google Scholar
[5]Johnson, J.. Remarks on Banach spaces of compact operators. J. Funct. Anal. 32 (1979), 304–311.Google Scholar
[6]Mach, J. and Ward, J. D.. Approximation by compact operators on certain Banach spaces. J. Approx. Theory 33 (1978), 274–286.Google Scholar
[7]Saatkamp, K.. M-ideals of compact operators. Math. Z. 158 (1978), 253–263.Google Scholar