TY - JOUR T1 - On the Quotients of Regular Operators AU - Bayram, Erdal AU - Binbaşıoğlu, Cansu Binnaz PY - 2019 DA - March Y2 - 2019 DO - 10.32323/ujma.509358 JF - Universal Journal of Mathematics and Applications JO - Univ. J. Math. Appl. PB - Emrah Evren KARA WT - DergiPark SN - 2619-9653 SP - 44 EP - 47 VL - 2 IS - 1 LA - en AB - 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. KW - Regular operators KW - L-weakly compact operator KW - M-weakly compact operator KW - Banach lattice KW - Quotient space KW - Regular operators CR - [1] E. Bayram, A. W. Wickstead, Banach lattices of L-weakly and M-weakly compact operators, Arch. Math. (Basel) 108(2017), 293–299. CR - [2] H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1974. CR - [3] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985. CR - [4] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991. CR - [5] W. Wnuk, Banach Lattices with Order Continuous Norms, Advenced Topics in Mathematics, Polish Scientific Publishers PWN, Warsaw, 1999. CR - [6] A. W. Wickstead, Regular operators between Banach lattices, Positivity, TrendsMath., Birkhauser, Basel, 2007. CR - [7] W. A. J. Luxemburg, A.C. Zaanen, Riesz Spaces I, North-Holland Publ., Amsterdam, 1971. CR - [8] Z. L. Chen and A. W. Wickstead, L-weakly and M-weakly compact operators, Indag. Math. (N.S.), 10(3) (1999), 321-336. CR - [9] E. Bayram , W. Wnuk, Some Algebra Ideals Of Regular Operators, Comment. Math. 532 (2013), 127-133. CR - [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. CR - [11] M. Wojtowicz, Copies of $\ell _{\infty }$ in quotients of locally solid Riesz spaces, Arch. Math. 80(2003), 294–301. CR - [12] M. Gonzalez, E. Saksman, H.O. Tylli, Representing non-weakly compact operators, Studia Math., 113 (1995), 265-282. UR - https://doi.org/10.32323/ujma.509358 L1 - https://dergipark.org.tr/en/download/article-file/675367 ER -