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2001 ON THE EXTENSION OF k-NUC NORMS
Khaing Khaing Aye, Wee-Kee Tang
Taiwanese J. Math. 5(2): 317-321 (2001). DOI: 10.11650/twjm/1500407339

Abstract

It is well-known that if Y is a closed subspace of a separable Banach space X; and if Y admits a locally uniformly rotund (LUR) norm, then this LUR norm on Y can be extended to a LUR norm on X: (See [4,5] and II.8 of [1].) In [2], Fabian used a new technique to extend the result to other forms of rotundity without requiring X to be separable. However in [2], the subpace Y has to be reflexive. The second-named author later showed that the condition that Y is reflexive could be removed. (See [8] and [9].) It is worth noting that the techniques used in the above three instances are completely different and each has its own strength. Fabian’s extension preserves moduli of convexity of power type. The extension given in [8] is simple and turns out to be very useful in many situations.

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Khaing Khaing Aye. Wee-Kee Tang. "ON THE EXTENSION OF k-NUC NORMS." Taiwanese J. Math. 5 (2) 317 - 321, 2001. https://doi.org/10.11650/twjm/1500407339

Information

Published: 2001
First available in Project Euclid: 18 July 2017

zbMATH: 0987.46010
MathSciNet: MR1832170
Digital Object Identifier: 10.11650/twjm/1500407339

Rights: Copyright © 2001 The Mathematical Society of the Republic of China

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