- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- Two problems in the theory of disjointness preserving operators
Two problems in the theory of disjointness preserving operators
Authors : Bahri Turan, Kazim Özcan
Pages : 361-364
Doi:10.15672/hujms.622718
View : 11 | Download : 14
Publication Date : 2021-04-11
Article Type : Research
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].Keywords : Riesz space, disjointness preserving operator, Hart's Theorem