Twisted sums of sequence spaces and the three space problem

Kalton, N. J.; Peck, N. T.

doi:10.1090/S0002-9947-1979-0542869-X

Twisted sums of sequence spaces and the three space problem
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by N. J. Kalton and N. T. Peck

Trans. Amer. Math. Soc. 255 (1979), 1-30

DOI: https://doi.org/10.1090/S0002-9947-1979-0542869-X

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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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