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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

Two problems in the theory of disjointness preserving operators

Bahri Turan(Gazı University)0000-0001-5256-1115
Kazim Özcan(Gazi Highschool)0000-0002-4331-0792
Pages
—
Publication Date
2021-04-11
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Kitover in [Inverses of disjointness preserving operators, Mem.

📌 3 Key Takeaways

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Objective & Hypothesis:In this short note, our aim is to solve two problems in the theory of disjointness preserving operators.
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Key Findings & Data:Hart, Some properties of disjointness preserving operators, Mathematics Proceedings, 1985].
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Conclusion & Impact:Kitover in [Inverses of disjointness preserving operators, Mem.
🔬Design:Research Article
📍Scope:2000 Verileri
⚙️Variables:Riesz space · disjointness preserving operator · Hart's Theorem

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].

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Cite This Article

Turan, B., Özcan, K. (2021). Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.622718

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References (8)

  1. Y.A. Abramovich and A.K. Kitover, Inverses of disjointness preserving operators, Mem. Amer. Math. Soc. 143 (679), 2000.
  2. C.D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, London,1985.
  3. D.R. Hart, Some properties of disjointness preserving operators, Mathematics Proceedings A 88 (2), 183-197, 1985.
  4. W.A.J. Luxemburg and A.C. Zaanen, Riesz Space I, North Holland, Amsterdam, 1971.
  5. A.G. Rugy, La structure ideale des M-espaces, J. Math. Pures at Appl. 51, 331-373, 1972.
  6. H.H. Schaefer, Banach lattices and positive operators, Springer, Berlin, 1991.
  7. B. Turan, On ideal operators, Positivity 7, 141-148, 2003.
  8. A.C. Zaanen, Riesz spaces II, North-Holland, Amsterdam, 1983.