Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank

被引：0

作者：

Julio Becerra Guerrero

Ginés López Pérez

Antonio M. Peralta

A Rodríguez-Palacios

机构：

[1] Facultad de Ciencias,Universidad de Granada

[2] Facultad de Ciencias,Universidad de Granada

来源：

Mathematische Annalen | 2004年 / 330卷

关键词：

Hilbert Space; Banach Space; Open Subset; Unit Ball; Closed Ball;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove that, given a real JB*-triple X, there exists a nonempty relatively weakly open subset of the closed unit ball of X with diameter less than 2 (if and) only if the Banach space of X is isomorphic to a Hilbert space. Moreover we give the structure of real JB*-triples whose Banach spaces are isomorphic to Hilbert spaces. Such real JB*-triples are also characterized in two different purely algebraic ways.

引用

页码：45 / 58

页数：13

共 17 条

[1] Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank
Guerrero, JB
Pérez, GL
Peralta, AM
Rodríguez-Palacios, A
MATHEMATISCHE ANNALEN, 2004, 330 (01) : 45 - 58
[2] Relatively weakly open sets in closed balls of Banach spaces, and the centralizer
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MATHEMATISCHE ZEITSCHRIFT, 2009, 262 (03) : 557 - 570
[3] Relatively weakly open sets in closed balls of Banach spaces, and the centralizer
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Angel Rodríguez-Palacios
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[4] Relatively weakly open sets in closed balls of C*-algebras
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[9] Banach spaces in which weakly p-Dunford–Pettis sets are relatively compact
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Monatshefte für Mathematik, 2020, 191 : 719 - 733
[10] Banach spaces in which weakly p-Dunford-Pettis sets are relatively compact
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