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Year 2021, Volume: 50 Issue: 2, 361 - 364, 11.04.2021
https://doi.org/10.15672/hujms.622718

Abstract

References

  • [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.

Two problems in the theory of disjointness preserving operators

Year 2021, Volume: 50 Issue: 2, 361 - 364, 11.04.2021
https://doi.org/10.15672/hujms.622718

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].

References

  • [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.
There are 8 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Bahri Turan 0000-0001-5256-1115

Kazim Özcan This is me 0000-0002-4331-0792

Publication Date April 11, 2021
Published in Issue Year 2021 Volume: 50 Issue: 2

Cite

APA Turan, B., & Özcan, K. (2021). Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics, 50(2), 361-364. https://doi.org/10.15672/hujms.622718
AMA Turan B, Özcan K. Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics. April 2021;50(2):361-364. doi:10.15672/hujms.622718
Chicago Turan, Bahri, and Kazim Özcan. “Two Problems in the Theory of Disjointness Preserving Operators”. Hacettepe Journal of Mathematics and Statistics 50, no. 2 (April 2021): 361-64. https://doi.org/10.15672/hujms.622718.
EndNote Turan B, Özcan K (April 1, 2021) Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics 50 2 361–364.
IEEE B. Turan and K. Özcan, “Two problems in the theory of disjointness preserving operators”, Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, pp. 361–364, 2021, doi: 10.15672/hujms.622718.
ISNAD Turan, Bahri - Özcan, Kazim. “Two Problems in the Theory of Disjointness Preserving Operators”. Hacettepe Journal of Mathematics and Statistics 50/2 (April 2021), 361-364. https://doi.org/10.15672/hujms.622718.
JAMA Turan B, Özcan K. Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics. 2021;50:361–364.
MLA Turan, Bahri and Kazim Özcan. “Two Problems in the Theory of Disjointness Preserving Operators”. Hacettepe Journal of Mathematics and Statistics, vol. 50, no. 2, 2021, pp. 361-4, doi:10.15672/hujms.622718.
Vancouver Turan B, Özcan K. Two problems in the theory of disjointness preserving operators. Hacettepe Journal of Mathematics and Statistics. 2021;50(2):361-4.