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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Twisted sums of sequence spaces and the three space problem
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by N. J. Kalton and N. T. Peck PDF
Trans. Amer. Math. Soc. 255 (1979), 1-30 Request permission

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
  • © Copyright 1979 American Mathematical Society
  • 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