Two problems in the theory of disjointness preserving operators

Authors : Bahri TURAN, Kazim ÖZCAN

Pages : 361-364

Doi:10.15672/hujms.622718

View : 16 | Download : 6

Publication Date : 2021-04-11

Article Type : Research Paper

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