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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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Keywords: Banach lattice, disjointness preserving operator
Article copyright: © Copyright 1995 American Mathematical Society