Twisted sums of sequence spaces and the three space problem

Author:

Kalton N. J.,Peck N. T.

Abstract

In this paper we study the following problem: given a complete locally bounded sequence space Y, construct a locally bounded space Z with a subspace X such that both X and Z / X Z/X are isomorphic to Y, and such that X is uncomplemented in Z. We give a method for constructing Z under quite general conditions on Y, and we investigate some of the properties of Z. In particular, when Y is l p ( 1 > p > ) {l_p}\,(1\, > \,p\, > \,\infty ) , we identify the dual space of Z, we study the structure of basic sequences in Z, and we study the endomorphisms of Z and the projections of Z on infinite-dimensional subspaces.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference13 articles.

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4. M. I. Kadec and A. Pełcyzński, Bases, lacunary series and complemented subspaces in the spaces 𝐿_{𝑝}, Studia Math. 21 (1962), 161-176.

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