Operators on C[0,1] preserving copies of asymptotic l1 spaces

被引：6

作者：

Gasparis, I ^{[1
]}

机构：

[1] Aristotle Univ Thessaloniki, Dept Math, Thessaloniki 54124, Greece

来源：

MATHEMATISCHE ANNALEN | 2005年 / 333卷 / 04期

关键词：

Operators on C(K) space; asymptotic l(1) space; weakly null sequence; Schreier sets;

D O I：

10.1007/s00208-005-0702-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given separable Banach spaces X, Y, Z and a bounded linear operator T:X -> Y, then T is said to preserve a copy of Z provided that there exists a closed linear subspace E of X isomorphic to Z and such that the restriction of T to E is an into isomorphism. It is proved that every operator on C([0,1]) which preserves a copy of an asymptotic l(1) space also preserves a copy of C([0,1]).

引用

页码：831 / 858

页数：28

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