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On the Quotients of Regular Operators

Year 2019, Volume: 2 Issue: 1, 44 - 47, 20.03.2019
https://doi.org/10.32323/ujma.509358

Abstract

We give some results about quotients of regular operators on Banach lattices by the linear span of the positive M-weakly and positive L-weakly compact operators. We also present a representation of the quotient space created by the linear span of the positive L-weakly compact operators.

References

  • [1] E. Bayram, A. W. Wickstead, Banach lattices of L-weakly and M-weakly compact operators, Arch. Math. (Basel) 108(2017), 293–299.
  • [2] H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
  • [3] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985.
  • [4] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991.
  • [5] W. Wnuk, Banach Lattices with Order Continuous Norms, Advenced Topics in Mathematics, Polish Scientific Publishers PWN, Warsaw, 1999.
  • [6] A. W. Wickstead, Regular operators between Banach lattices, Positivity, TrendsMath., Birkhauser, Basel, 2007.
  • [7] W. A. J. Luxemburg, A.C. Zaanen, Riesz Spaces I, North-Holland Publ., Amsterdam, 1971.
  • [8] Z. L. Chen and A. W. Wickstead, L-weakly and M-weakly compact operators, Indag. Math. (N.S.), 10(3) (1999), 321-336.
  • [9] E. Bayram , W. Wnuk, Some Algebra Ideals Of Regular Operators, Comment. Math. 532 (2013), 127-133.
  • [10] Z. L. Chen, Y. Feng, J.X. Chen, The Order Continuity of the Regular Norm on Regular Operator Spaces, Abstr. Appl. Anal., (2013), Article ID 183786, 7 pages.
  • [11] M. Wojtowicz, Copies of $\ell _{\infty }$ in quotients of locally solid Riesz spaces, Arch. Math. 80(2003), 294–301.
  • [12] M. Gonzalez, E. Saksman, H.O. Tylli, Representing non-weakly compact operators, Studia Math., 113 (1995), 265-282.
Year 2019, Volume: 2 Issue: 1, 44 - 47, 20.03.2019
https://doi.org/10.32323/ujma.509358

Abstract

References

  • [1] E. Bayram, A. W. Wickstead, Banach lattices of L-weakly and M-weakly compact operators, Arch. Math. (Basel) 108(2017), 293–299.
  • [2] H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974.
  • [3] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985.
  • [4] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991.
  • [5] W. Wnuk, Banach Lattices with Order Continuous Norms, Advenced Topics in Mathematics, Polish Scientific Publishers PWN, Warsaw, 1999.
  • [6] A. W. Wickstead, Regular operators between Banach lattices, Positivity, TrendsMath., Birkhauser, Basel, 2007.
  • [7] W. A. J. Luxemburg, A.C. Zaanen, Riesz Spaces I, North-Holland Publ., Amsterdam, 1971.
  • [8] Z. L. Chen and A. W. Wickstead, L-weakly and M-weakly compact operators, Indag. Math. (N.S.), 10(3) (1999), 321-336.
  • [9] E. Bayram , W. Wnuk, Some Algebra Ideals Of Regular Operators, Comment. Math. 532 (2013), 127-133.
  • [10] Z. L. Chen, Y. Feng, J.X. Chen, The Order Continuity of the Regular Norm on Regular Operator Spaces, Abstr. Appl. Anal., (2013), Article ID 183786, 7 pages.
  • [11] M. Wojtowicz, Copies of $\ell _{\infty }$ in quotients of locally solid Riesz spaces, Arch. Math. 80(2003), 294–301.
  • [12] M. Gonzalez, E. Saksman, H.O. Tylli, Representing non-weakly compact operators, Studia Math., 113 (1995), 265-282.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Erdal Bayram 0000-0001-8488-359X

Cansu Binnaz Binbaşıoğlu This is me

Publication Date March 20, 2019
Submission Date January 7, 2019
Acceptance Date February 26, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Bayram, E., & Binbaşıoğlu, C. B. (2019). On the Quotients of Regular Operators. Universal Journal of Mathematics and Applications, 2(1), 44-47. https://doi.org/10.32323/ujma.509358
AMA Bayram E, Binbaşıoğlu CB. On the Quotients of Regular Operators. Univ. J. Math. Appl. March 2019;2(1):44-47. doi:10.32323/ujma.509358
Chicago Bayram, Erdal, and Cansu Binnaz Binbaşıoğlu. “On the Quotients of Regular Operators”. Universal Journal of Mathematics and Applications 2, no. 1 (March 2019): 44-47. https://doi.org/10.32323/ujma.509358.
EndNote Bayram E, Binbaşıoğlu CB (March 1, 2019) On the Quotients of Regular Operators. Universal Journal of Mathematics and Applications 2 1 44–47.
IEEE E. Bayram and C. B. Binbaşıoğlu, “On the Quotients of Regular Operators”, Univ. J. Math. Appl., vol. 2, no. 1, pp. 44–47, 2019, doi: 10.32323/ujma.509358.
ISNAD Bayram, Erdal - Binbaşıoğlu, Cansu Binnaz. “On the Quotients of Regular Operators”. Universal Journal of Mathematics and Applications 2/1 (March 2019), 44-47. https://doi.org/10.32323/ujma.509358.
JAMA Bayram E, Binbaşıoğlu CB. On the Quotients of Regular Operators. Univ. J. Math. Appl. 2019;2:44–47.
MLA Bayram, Erdal and Cansu Binnaz Binbaşıoğlu. “On the Quotients of Regular Operators”. Universal Journal of Mathematics and Applications, vol. 2, no. 1, 2019, pp. 44-47, doi:10.32323/ujma.509358.
Vancouver Bayram E, Binbaşıoğlu CB. On the Quotients of Regular Operators. Univ. J. Math. Appl. 2019;2(1):44-7.

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