Duality of the weak essential norm

Author:
Hans-Olav Tylli

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1437-1443

MSC (2000):
Primary 47A30, 46B20, 46B28

DOI:
https://doi.org/10.1090/S0002-9939-00-05937-2

Published electronically:
October 24, 2000

MathSciNet review:
1814170

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Abstract | References | Similar Articles | Additional Information

It is established by an example that the natural quotient norms and are not comparable in general. Hence there is no uniform quantitative version of Gantmacher's duality theorem for weakly compact operators in terms of the preceding weak essential norm. Above stands for the class of weakly compact operators , where and are Banach spaces. The counterexample is based on a renorming construction related to weakly compact approximation properties that is applied to the Johnson-Lindenstrauss space .

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Additional Information

**Hans-Olav Tylli**

Affiliation:
Department of Mathematics, University of Helsinki, P. O. Box 4 (Yliopistonkatu 5), FIN-00014 University of Helsinki, Finland

Email:
hojtylli@cc.helsinki.fi

DOI:
https://doi.org/10.1090/S0002-9939-00-05937-2

Received by editor(s):
August 17, 1999

Published electronically:
October 24, 2000

Communicated by:
Dale Alspach

Article copyright:
© Copyright 2000
American Mathematical Society