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A 3-space problem related to the fixed point property

Published online by Cambridge University Press:  17 April 2009

Helga Fetter  and
Berta Gamboa de Buen
Helga Fetter
Affiliation:
CIMAT, Apdo. Postal 402, 36000 Guanajuato, Gto. México
Berta Gamboa de Buen
Affiliation:
CIMAT, Apdo. Postal 402, 36000 Guanajuato, Gto. México
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Abstract

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We study some properties which imply weak normal structure and thus the fixed point property. We investigate whether the latter two properties are inherited by spaces obtained by direct sum with a finite dimensional space. We exhibit a space X which satisfies Opial's condition, X ⊕ ℝ does not have weak normal structure but X ⊕ ℝ has the fixed point property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 51 - 61
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bynum, W.L., ‘Normal structure coefficients for Banach spaces’, Pacific J. Math. 86 (1980), 427–436.CrossRefGoogle Scholar
[2]Goebel, K. and Kirk, W.A., Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics 28 (Cambridge University Press, Cambridge, 1990).CrossRefGoogle Scholar
[3]Gossez, J.P. and Dozo, E. Lami, ‘Structure normale et base de Schauder’, Acad. Roy. Belg. Bull. Cl. Sci. 55 (1969), 673–681.Google Scholar
[4]Landes, T., ‘Permanence properties of normal structure’, Pacific J. Math. 110 (1984), 125–143.CrossRefGoogle Scholar
[5]Landes, T., ‘Normal structure and the sum-property.’, Pacific J. Math. 123 (1986), 127–147.CrossRefGoogle Scholar
[6]Jiménez-Melado, A., ‘Stability of weak normal structure in James quasi reflexive space’, Bull Austral. Math. Soc. 46 (1992), 367–372.CrossRefGoogle Scholar
[7]Sims, B. and Smyth, M., ‘On non-uniform conditions giving weak normal structure’, Quaestiones Math. 18 (1995), 9–19.CrossRefGoogle Scholar
[8]Sims, B. and Smyth, M., ‘On some Banach space properties sufficient for weak normal structure and their permanence properties’, Trans. Amer. Math. Soc. 351 (1999), 497–513.CrossRefGoogle Scholar
[9]Tingley, D., ‘The normal structure of James quasi reflexive space’, Bull. Austral. Math. Soc. 42 (1990), 95–100.CrossRefGoogle Scholar