Two problems in the theory of disjointness preserving operators


TURAN B. , Ozcan K.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.50, sa.2, ss.361-364, 2021 (SCI İndekslerine Giren Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 50 Konu: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.15672/hujms.622718
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.361-364

Özet

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].