On Lindenstrauss-Pełczyński spaces

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dc.creatorCastillo, Jesús M. F.
dc.creatorMoreno, Yolanda
dc.creatorSuárez, Jesús
dc.date2005-02-04
dc.date2005-03-20
dc.date.accessioned2026-07-07T05:16:41Z
dc.date.available2026-07-07T05:16:41Z
dc.descriptionIn 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-Pełczyński 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.
dc.identifierhttps://arxiv.org/abs/math/0502081
dc.identifierhttp://arxiv.org/abs/math/0502081
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74078
dc.subjectFunctional Analysis
dc.subject46B03; 46M99; 46B07
dc.titleOn Lindenstrauss-Pełczyński spaces
dc.typetext

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