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# Twisted Sums of Sequence Spaces and the Three Space Problem

N. J. Kalton and N. T. Peck
Transactions of the American Mathematical Society
Vol. 255 (Nov., 1979), pp. 1-30
DOI: 10.2307/1998164
Stable URL: http://www.jstor.org/stable/1998164
Page Count: 30
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## 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 $Z / X$ 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 $l_p (1 < p < \infty)$, 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.

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