On the Quotients of Regular Operators
Year 2019,
Volume: 2 Issue: 1, 44 - 47, 20.03.2019
Erdal Bayram
,
Cansu Binnaz Binbaşıoğlu
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
Erdal Bayram
,
Cansu Binnaz Binbaşıoğlu
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.