Abstract
We give conditions for the linear span of the positive L-weakly compact (resp. M-weakly compact) operators to be a Banach lattice under the regular norm, for that Banach lattice to have an order continuous norm, to be an AL-space or an AM-space.
Article PDF
Similar content being viewed by others
References
C. D. Aliprantis and O. Burkinshaw, Positive Operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985.
C. D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, 2006. Reprint of the 1985 original.
Z. L. Chen and A. W. Wickstead, Equalities involving the modulus of an operator, Math. Proc. R. Ir. Acad. 99A (1999), 85–92.
Z. L. Chen and A. W. Wickstead, L-weakly and M-weakly compact operators, Indag. Math. (N.S.) 10 (1999), 321–336.
Z. L. Chen and A. W. Wickstead, The order properties of r-compact operators on Banach lattices, Acta Math. Sin. (Engl. Ser.) 23 (2007), 457–466.
P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991.
A. W. Wickstead, AL-spaces and AM-spaces of operators, Positivity 4 (2000), 303–311.
Author information
Authors and Affiliations
Corresponding author
Additional information
The first author was supported by The Scientific and Technological Research Council of Turkey (TUBITAK) within the context of 2219-Post Doctoral Fellowship Program and by the Research Foundation of Namik Kemal University (Project No.NKUBAP.00.10.AR.15.04.).
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bayram, E., Wickstead, A.W. Banach lattices of L-weakly and M-weakly compact operators. Arch. Math. 108, 293–299 (2017). https://doi.org/10.1007/s00013-017-1026-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-017-1026-3