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On the failure of close-to-normal
structure type conditions
and pathological Kannan maps


Author: Michael A. Smyth
Journal: Proc. Amer. Math. Soc. 124 (1996), 3063-3069
MSC (1991): Primary 46B20, 47H09
DOI: https://doi.org/10.1090/S0002-9939-96-03466-1
MathSciNet review: 1342047
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the failure of close-to-normal structure type conditions and show that a Banach space can be renormed to fail close-to-weak normal structure exactly when it contains a norm inseparable weakly compact subset. Included is an example of a particularly pathological fixed point free Kannan map.


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Additional Information

Michael A. Smyth
Affiliation: Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Address at time of publication: 1 Frost Rd., Mt. Roskill, Auckland, New Zealand

DOI: https://doi.org/10.1090/S0002-9939-96-03466-1
Received by editor(s): February 23, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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