Abstract
Abstract
The classical Banach space
$L_1(L_p)$
consists of measurable scalar functions f on the unit square for which
$$ \begin{align*}\|f\| = \int_0^1\Big(\int_0^1 |f(x,y)|^p dy\Big)^{1/p}dx < \infty.\end{align*} $$
We show that
$L_1(L_p) (1 < p < \infty )$
is primary, meaning that whenever
$L_1(L_p) = E\oplus F$
, 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.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献