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2015 Diameter two properties in James spaces
Julio Becerra Guerrero, Gines Lopez-Perez, Abraham Rueda Zoca
Banach J. Math. Anal. 9(4): 203-220 (2015). DOI: 10.15352/bjma/09-4-10

Abstract

We study the diameter two properties in the (James type) Banach spaces $JH$, $JT_\infty$ and $JH_\infty$. We show that the dual spaces of these three Banach spaces fail every diameter two property. Also, we prove that $JH$ and $JH_{\infty}$ satisfy the strong diameter two property, and so the dual norms of these spaces are octahedral. In addition, we find a closed hyperplane $M$ of $JH_\infty$ such that its dual space, $M^*$, satisfies the $w^*$-strong diameter two property. Finally, we get that the natural norms of $M$ and $M^*$ are octahedral.

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Julio Becerra Guerrero. Gines Lopez-Perez. Abraham Rueda Zoca. "Diameter two properties in James spaces." Banach J. Math. Anal. 9 (4) 203 - 220, 2015. https://doi.org/10.15352/bjma/09-4-10

Information

Published: 2015
First available in Project Euclid: 17 April 2015

zbMATH: 1329.46012
MathSciNet: MR3336889
Digital Object Identifier: 10.15352/bjma/09-4-10

Subjects:
Primary: 46B20
Secondary: 46B22 , 52A10

Keywords: diameter two properties , James space , octahedral norm

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.9 • No. 4 • 2015
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