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Copies of l∞ in an operator space

Published online by Cambridge University Press:  24 October 2008

Lech Drewnowski
Lech Drewnowski
Affiliation:
Institute of Mathematics, A. Mickiewicz University, Poznan, Poland
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Extract

Let X and Y be Banach spaces. Then Kw*(X*, Y) denotes the Banach space of compact and weak*-weakly continuous linear operators from X* into Y, endowed with the usual operator norm. Let us write E⊃l∞ to indicate that a Banach space E contains an isomorphic copy of l∞. The purpose of this note is to prove the following

Theorem. Kw*(X*, Y) ⊃ l∞if and only if either X ⊃ l∞or Y ⊃ l∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 3 , November 1990 , pp. 523 - 526
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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