Strategically reproducible bases and the factorization property

被引：10

作者：

Lechner, Richard ^{[1
]}

Motakis, Pavlos ^{[2
]}

Mueller, Paul F. X. ^{[1
]}

Schlumprecht, Thomas ^{[3
]}

机构：

[1] Johannes Kepler Univ Linz, Inst Anal, Altenberger Str 69, A-4040 Linz, Austria

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2020年 / 238卷 / 01期

基金：

奥地利科学基金会; 美国国家科学基金会;

关键词：

LESS-THAN; SPACES; PROJECTIONS; H-1;

D O I：

10.1007/s11856-020-2011-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the concept of strategically reproducible bases in Banach spaces and show that operators which have large diagonal with respect to strategically reproducible bases are factors of the identity. We give several examples of classical Banach spaces in which the Haar system is strategically reproducible: multi-parameter Lebesgue spaces, mixed-norm Hardy spaces and most significantly the space L-1. Moreover, we show the strategical reproducibility is inherited by unconditional sums.

引用

页码：13 / 60

页数：48

共 25 条

[1]

ALSPACH D, 1977, STUD MATH, V60, P79

[2]

ANDREW AD, 1979, STUD MATH, V65, P288

[3] A study of conditional spreading sequences [J].