The space L1(Lp) is primary for 1 < p < ∞

被引：2
|
作者：
Lechner, Richard [1 ]
Motakis, Pavlos [2 ]
Mueller, Paul F. X. [1 ]
Schlumprecht, Thomas [3 ,4 ]
机构：
[1] Johannes Kepler Univ Linz, Inst Anal, Altenberger Str 69, A-4040 Linz, Austria
[2] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada
[3] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
[4] Czech Tech Univ, Fac Elect Engn, Zikova 4, Prague 16627, Czech Republic
来源：
FORUM OF MATHEMATICS SIGMA | 2022年 / 10卷
基金：
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
MULTIPLIERS; LP; SUBSPACES;
D O I：
10.1017/fms.2022.25
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The classical Banach space L-1 (L-p) consists of measurable scalar functions f on the unit square for which parallel to integral parallel to = integral(1)(0) (integral(1)(0) vertical bar f(x, y)vertical bar(p) dy)(1/p) dx < infinity. We show that L-1(L-p) (1 < p < infinity) is primary, meaning that whenever L-1(L-p) = E circle plus F, where E and F are closed subspaces of L-1(L-p), then either E or F is isomorphic to L-1(L-p). More generally, we show that L-1 (X) is primary for a large class of rearrangement-invariant Banach function spaces.
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页数：36
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