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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Hammerstein operators preserving disjointness
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by A. V. Koldunov PDF
Proc. Amer. Math. Soc. 123 (1995), 1083-1095 Request permission

Abstract:

This paper deals with the problems of a multiplicative representation and of automatic continuity of linear and nonlinear operators preserving disjointness. The operators satisfying a modified Hammerstein condition are introduced and investigated. In §3 we develop a theory of quasi-linear disjointness-preserving Hammerstein operators. As an application we prove that a bijective disjointness-preserving operator between Banach lattices is a continuous d-isomorphism, thus answering in the affirmative a problem posed by Y. Abramovich in 1992. We also construct an example demonstrating that the completeness of the "departure" space cannot be omitted in general.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1083-1095
  • MSC: Primary 47B65; Secondary 46A40, 46B42, 47H99
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1212284-9
  • MathSciNet review: 1212284