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The approximation problem for compact operators

Published online by Cambridge University Press:  17 April 2009

S.R. Caradus
S.R. Caradus
Affiliation:
Department of Mathematics, IAS, Australian National University, Canberra, ACT, and Queen's University at Kingston, Ontario, Canada.
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Abstract

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The following sufficient condition is obtained for the uniform approximability of compact operators on a reflexive Banach space by operators of finite rank: if S is the unit ball of X and ø: X* → C(S) is the imbedding ø(x*)x = x*(x) then we require ø(X*) to be complemented in C(S).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 397 - 401
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Goldberg, Seymour, Unbounded linear operators (McGraw-Hill, New York, 1966).Google Scholar
[2]Grothendieck, Alexandre, “Produits tensoriels topologiques et espaces nucléaires”, Mem. Amer. Math. Soc. 16 (1995).Google Scholar
[3]Lindenstrauss, Joram, “Extension of compact operators”, Mem. Amer. Math. Soc. 48 (1964).Google Scholar