Two problems in the theory of disjointness preserving operators
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.50, no.2, pp.361-364, 2021 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 50 Issue: 2
- Publication Date: 2021
- Doi Number: 10.15672/hujms.622718
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.361-364
- Gazi University Affiliated: Yes
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].