This is an announcement for the paper "On Lindenstrauss-Pelczynski spaces" by Jesus M. F. Castillo, Yolanda Moreno and Jesus Suarez.
Abstract: In this work we shall be concerned with some stability aspects of the classical problem of extension of $C(K)$-valued operators. We introduce the class $\mathscr{LP}$ of Banach spaces of Lindenstrauss-Pe\l czy'{n}sky type as those such that every operator from a subspace of $c_0$ into them can be extended to $c_0$. We show that all $\mathscr{LP}$-spaces are of type $\mathcal L_\infty$ but not the converse. Moreover, $\mathcal L_\infty$-spaces will be characterized as those spaces $E$ such that $E$-valued operators from $w^*(l_1,c_0)$-closed subspaces of $l_1$ extend to $l_1$. Complemented subspaces of $C(K)$ and separably injective spaces are subclasses of $\mathscr{LP}$-spaces and we show that the former does not contain the latter. It is established that $\mathcal L_\infty$-spaces not containing $l_1$ are quotients of $\mathscr{LP}$-spaces, while $\mathcal L_\infty$-spaces not containing $c_0$, quotients of an $\mathscr{LP}$-space by a separably injective space and twisted sums of $\mathscr{LP}$-spaces are $\mathscr{LP}$-spaces.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B03; 46M99; 46B07
The source file(s), CastilloMorenoLP.tex: 49873 bytes, is(are) stored in gzipped form as 0502081.gz with size 15kb. The corresponding postcript file has gzipped size 72kb.
Submitted from: castillo@unex.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/math.FA/0502081
or
http://arXiv.org/abs/math.FA/0502081
or by email in unzipped form by transmitting an empty message with subject line
uget 0502081
or in gzipped form by using subject line
get 0502081
to: math@arXiv.org.