Abstract
GOSSEZ and LAMI DOZO have obtained a sufficient condition for a Banach space with a Schauder basis to have normal structure. This paper generalizes their theorem to obtain a sufficient condition for an arbitrary Banach space to have normal structure. An example is given to show an application of the theorem.
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DAY, M. M.: Uniform convexity in factor and conjugate spaces. Annals of Math. 45, 375–385 (1944).
GOEBEL, K.: Convexity of balls and fixed point theorems for mappings with nonexpansive square. Compositio Math. 22, 269–274 (1970).
GOSSEZ, J. P. and LAMI DOZO, E.: Structure normale et base de Schauder. Bull. Acad. Royale Belgique (5e ser.) 55, 673–681 (1969).
JAMES, R. C.: Uniformly non-square Banach spaces. Annals of Math. 80, 542–550 (1964).
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Research supported by a Faculty Research Grant of the College of William and Mary.
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Bynum, W.L. Normal structure of banach spaces. Manuscripta Math 11, 203–209 (1974). https://doi.org/10.1007/BF01173714
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DOI: https://doi.org/10.1007/BF01173714