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Stably Dominated and Stably Regular Operators

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Vector Lattices and Integral Operators

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

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Abstract

This chapter is mainly devoted to studying those properties of Banach lattices and operators on them whose description requires the vector lattice structure as well as the pure Banach space structure. In particular, we study the properties of the operators acting between vector lattices and remaining to be order bounded under multiplication by arbitrary Banach endomorphisms in these lattices. In spite of being natural, such classes of operators have attracted very little attention of mathematicians. At present, the theory of p-absolutely summing operators plays a key role in solving the arising problems; in Sections 3.1–3.3 and 3.5, we briefly expose those results of the theory which are most important for us. The reader interested in a more complete presentation of the theory will refer to the monographs [42, 32, 45] and the articles [20, 22, 39].

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Authors
  1. B. M. Makarov
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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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Makarov, B.M. (1996). Stably Dominated and Stably Regular 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_3

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  • DOI: https://doi.org/10.1007/978-94-009-0195-7_3

  • 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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