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<p>In the theory of Riesz spaces or pre-Riesz spaces, a classical problem is the following: Given a disjointness preserving bijection between such spaces, is then the inverse again disjointness preserving? This is valid, e.g., in Banach lattices or finite-dimensional pre-Riesz spaces. Similar results on inverses of bijections were also given for special classes of disjointness preserving operators, e.g., Riesz* homomorphisms or complete Riesz homomorphisms. In this paper, we address analogous problems for generalized inverses, focusing particularly on the Drazin inverse. We generalize some of the classical results to this new setting.</p>

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Generalized inverses of disjointness preserving linear operators on pre-Riesz spaces

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Anke Kalauch,
  • Pavankumar Raickwade,
  • K. C. Sivakumar

摘要

In the theory of Riesz spaces or pre-Riesz spaces, a classical problem is the following: Given a disjointness preserving bijection between such spaces, is then the inverse again disjointness preserving? This is valid, e.g., in Banach lattices or finite-dimensional pre-Riesz spaces. Similar results on inverses of bijections were also given for special classes of disjointness preserving operators, e.g., Riesz* homomorphisms or complete Riesz homomorphisms. In this paper, we address analogous problems for generalized inverses, focusing particularly on the Drazin inverse. We generalize some of the classical results to this new setting.