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On the Quotients of Regular Operators

Year 2019, , 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, , 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

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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