Direct sums of renormings of l1 and the fixed point property

被引：4

作者：

Dowling, P. N. ^{[2
]}

Lin, Pei-Kee ^{[3
]}

Turett, B. ^{[1
]}

机构：

[1] Oakland Univ, Dept Math & Stat, Rochester, MI 48309 USA

[2] Miami Univ, Dept Math, Oxford, OH 45056 USA

[3] Univ Memphis, Dept Math, Memphis, TN 38152 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 03期

关键词：

Renorming; Fixed point property; NONEXPANSIVE-MAPPINGS;

D O I：

10.1016/j.na.2010.03.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let gamma(n) be an increasing sequence in (0, 1) that converges to 1, and let parallel to vertical bar.parallel to vertical bar be the equivalent norm of l(1) defined by parallel to vertical bar(a(k))parallel to vertical bar = sup(n is an element of N) gamma(n) Sigma(infinity)(k=n) |a(k)|. In this article, we show that for any m > 1, the space (Sigma(m)(l-1)circle plus(l(1), parallel to vertical bar.parallel to vertical bar)(1) is not isometrically isomorphic to any subspace of (l(1), parallel to vertical bar.parallel to vertical bar) and it has the fixed point property. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：591 / 599

页数：9

共 8 条

[1]

Dowling PN, 2001, HANDBOOK OF METRIC FIXED POINT THEORY, P269

[2]

FETTER H, COMMUNICATION

[3]

Kirk W.A., 2001, Handbook of Metric Fixed Point Theory

[4]

KIRK WA, 1984, HOUSTON J MATH, V10, P207