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Smoothness in spaces of compact operators

Published online by Cambridge University Press:  17 April 2009

A. Sersouri
A. Sersouri
Affiliation:
Equipe d'analyse, U.A. No. 754 au C.N.R.S., Université Paris VI, Tour 46 - 4ème Etage, 4, Place Jussieu, 75252 - Paris Cedex 05
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Abstract

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We prove that if X and Y are two (real) Banach spaces such that dim X ≥ 2 and dim Y ≥ 2, then the space K(X, Y) contains a convex compact subset C with dim C ≥ 2 (in the affine sense) which fails to be an intersection of balls. This improves two results of Ruess and Stegall.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 2 , April 1988 , pp. 221 - 225
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Lewis, D.R., ‘Ellipsoids defined by Banach ideal norms’, Mathematika 28 (1979), 18–29.CrossRefGoogle Scholar
[2]Ruess, W.M. and Stegall, C.P., ‘Exposed and denting points in duals of operator spaces’, Israel J. Math. 53 (1986), 163–190.CrossRefGoogle Scholar
[3]Sersouri, A., ‘Mazur property for compact sets’, (Preprint).Google Scholar
[4]Sersouri, A., ‘Mazur property for finite dimensional sets’, (Preprint).Google Scholar
[5]Whitefield, J.H.M. and Zizier, V., ‘Mazur's intersection property of balls for compact convex sets’, Bull. Austral. Math. Soc. 35 (1987), 267–274.CrossRefGoogle Scholar