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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hammerstein operators preserving disjointness


Author: A. V. Koldunov
Journal: Proc. Amer. Math. Soc. 123 (1995), 1083-1095
MSC: Primary 47B65; Secondary 46A40, 46B42, 47H99
MathSciNet review: 1212284
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1212284-9
PII: S 0002-9939(1995)1212284-9
Keywords: Banach lattice, disjointness preserving operator
Article copyright: © Copyright 1995 American Mathematical Society