Little Grothendieck's theorem for sublinear operators

被引：4
|
作者：
Achour, D [1 ]
Mezrag, L [1 ]
机构：
[1] Msilia Univ, Dept Math, Msila 28105, Algeria
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2004年 / 296卷 / 02期
关键词：
Banach lattice; sublinear operator; p-summing operator; p-regular operator;
D O I：
10.1016/j.jmaa.2004.04.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let SB(X, Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider pi(2)(X, Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K), H) is in pi(2) (C(K), H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open. (C) 2004 Elsevier Inc. All rights reserved.
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页码：541 / 552
页数：12
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