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Disjointness Preserving Operators

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Vector Lattices and Integral Operators

Part of the book series: Mathematics and Its Applications ((MAIA,volume 358))

Abstract

Disjointness preserving operators have its own theory which is very rich in results and includes such questions as boundedness, continuity, spectral and geometric properties, multiplicativity, compactness, etc. The list of publications devoted to studying disjointness preserving operators is so extensive that it could serve as a reason for a separate review. Leaving aside many rather interesting directions, we will only concentrate our attention on analytic representation and decomposition of disjointness preserving operators. B.Z. Vulikh [7–9] was one of the first who considered these questions. Later, disjointness preserving operators were studied by Yu. A. Abramovich, E. L. Arenson, D. R. Hart, A. K. Kitover, A. V. Koldunov, P. T. N. MacPolin, A. I. Veksler, A. W. Wickstead, A. C. Zaanen, and many others (see, for instance, [1–3, 19, 32, 37, 41, 42]). We also observe that the question of analytic representation of disjointness preserving operators includes such a powerful direction as descriptions of isometries of vector-valued L P-spaces (the so-called Banach-Stone theorems).

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Authors
  1. A. E. Gutman
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Editors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Siberia, Russia

    S. S. Kutateladze

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© 1996 Kluwer Academic Publishers

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Gutman, A.E. (1996). Disjointness Preserving Operators. In: Kutateladze, S.S. (eds) Vector Lattices and Integral Operators. Mathematics and Its Applications, vol 358. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0195-7_5

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  • DOI: https://doi.org/10.1007/978-94-009-0195-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6571-9

  • Online ISBN: 978-94-009-0195-7

  • eBook Packages: Springer Book Archive

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