Two problems in the theory of disjointness preserving operators


TURAN B. , Ozcan K.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.2, pp.361-364, 2021 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.15672/hujms.622718
  • Title of Journal : HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Page Numbers: pp.361-364

Abstract

In this short note, our aim is to solve two problems in the theory of disjointness preserving operators. Firstly, we obtain the converse direction of Hart's Theorem which was given in [D.R. Hart, Some properties of disjointness preserving operators, Mathematics Proceedings, 1985]. As a result, we get an affirmative solution of an open problem given by Y.A. Abramovich and A.K. Kitover in [Inverses of disjointness preserving operators, Mem. Amer. Math. Soc., 2000].