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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Twisted sums of sequence spaces and the three space problem


Authors: N. J. Kalton and N. T. Peck
Journal: Trans. Amer. Math. Soc. 255 (1979), 1-30
MSC: Primary 46A45
DOI: https://doi.org/10.1090/S0002-9947-1979-0542869-X
MathSciNet review: 542869
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0542869-X
Keywords: Locally bounded space, Banach space, sequence space, uncomplemented subspace, three space problem, projection, strictly singular (co-singular) operator
Article copyright: © Copyright 1979 American Mathematical Society