2005/02/04 by Jesús M. F. Castillo, Castillo, Jesús M. F., Yolanda Moreno +3
Mathematics · #46B03 #46B07 #46M99 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #math.FA #msc:46B03 #msc:46B07 #msc:46M99
paper · pdf · doi:10.48550/arxiv.math/0502081
openalex publication_date 2005/02/04 · arxiv created 2005/03/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 \mathscrLP of Banach spaces of Lindenstrauss-Pełczyński type as those such that every operator from a subspace of c0 into them can be extended to c0. We show that all \mathscrLP-spaces are of type \mathcal L_∞ but not the converse. Moreover, \mathcal L_∞-spaces will be characterized as those spaces E such that E-valued operators from w^*(l1,c0)-closed subspaces of l1 extend to l1. Complemented subspaces of C(K) and separably injective spaces are subclasses of \mathscrLP-spaces and we show that the former does not contain the latter. It is established that \mathcal L_∞-spaces not containing l1 are quotients of \mathscrLP-spaces, while \mathcal L_∞-spaces not containing c0, quotients of an \mathscrLP-space by a separably injective space and twisted sums of \mathscrLP-spaces are \mathscrLP-spaces.