Bijective Disjointness Preserving Operators

  • Yuri Abramovich
  • Arkady Kitover
Conference paper

Abstract

A linear operator T: XY between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements in Y. Let T: XY be a bijective disjointness preserving operator, and so the inverse operator T -1 exists. In this paper we discuss the most recent results regarding the following problem: when is T -1 disjointness preserving? Apart from presenting several counterexamples to this problem we also formulate many sufficient conditions for the affirmative answer to it.

Keywords

Lution 

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Yuri Abramovich
    • 1
  • Arkady Kitover
    • 2
  1. 1.Department of Mathematical SciencesIUPUIIndianapolisUSA
  2. 2.Department of MathematicsCCPPhiladelphiaUSA

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