Arens regularity of projective tensor products

被引：3

作者：

Rajpal, Vandana ^{[1
]}

Kumar, Ajay ^{[1
]}

机构：

[1] Univ Delhi, Dept Math, Delhi, India

来源：

ARCHIV DER MATHEMATIK | 2016年 / 107卷 / 05期

关键词：

Operator space projective tensor norm; Haagerup tensor norm; Arens regularity; C-ASTERISK-ALGEBRAS; SPACES;

D O I：

10.1007/s00013-016-0942-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For completely contractive Banach algebras A and B (respectively operator algebras A and B), the necessary and sufficient conditions for the operator space projective tensor product A (circle times) over cap B (respectively the Haagerup tensor product A circle times(h) B) to be Arens regular are obtained. Using the non-commutative Grothendieck inequality, we show that, for C*-algebras A and B, A circle times(gamma) B is Arens regular if A (circle times) over cap B and A (circle times) over cap B-op are Arens regular whereas A (circle times) over cap B is Arens regular if and only if A circle times h B and B circle times(h) A are, where circle times(h), circle times(gamma), and (circle times) over cap. are the Haagerup, the Banach space projective tensor norm, and the operator space projective tensor norm, respectively.

引用

页码：531 / 541

页数：11

共 18 条

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[2]

[Anonymous], 1990, Int. J. Math.

[3]

[Anonymous], 2000, OPERATOR SPACES

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