A remark on bases in quotients of
when ![0 < p < 1](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4aa551fbcfe97fbd4468f5d86a324a30.png)
Abstract
In [9] Stiles showed that if
has an infinite-dimensional closed subspace which contains no complemented copy of
; this contrasts with the well-known result of Pelczynski [5] for
. The following curious theorem is the main result of this note: Theorem 1. Let M be an infinite-dimensional closed subspace of
where
. Suppose
has a basis. Then M contains a subspace isomorphic to
and complemented in
.
![0 < p < 1, \ell<sub>p</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/715913e54acbe3420716c353304c2d20.png)
![\ell<sub>p</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/1174588500aeb3c5a13730bac47cf686.png)
![1≤ p < ∈fty](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c76dd04302fb80de84871aed56fb9495.png)
![\ell<sub>p</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/1174588500aeb3c5a13730bac47cf686.png)
![0 < p < 1](http://siba-ese.unile.it/plugins/generic/latexRender/cache/4aa551fbcfe97fbd4468f5d86a324a30.png)
![\ell<sub>p</sub>/M](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c1b31f7230dc7c5a85c23ec97f56609f.png)
![\ell<sub>p</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/1174588500aeb3c5a13730bac47cf686.png)
![\ell<sub>p</sub>](http://siba-ese.unile.it/plugins/generic/latexRender/cache/1174588500aeb3c5a13730bac47cf686.png)
DOI Code:
10.1285/i15900932v11p231
Full Text: PDF