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Pseudocomplémentation dans les espaces de Banach

Patric Rauch (1991)

Studia Mathematica

This paper introduces the following definition: a closed subspace Z of a Banach space E is pseudocomplemented in E if for every linear continuous operator u from Z to Z there is a linear continuous extension ū of u from E to E. For instance, every subspace complemented in E is pseudocomplemented in E. First, the pseudocomplemented hilbertian subspaces of L ¹ are characterized and, in L p with p in [1, + ∞[, classes of closed subspaces in which the notions of complementation and pseudocomplementation...

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.

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