• Login
    View Item 
    •   NWU-IR Home
    • Research Output
    • Faculty of Natural and Agricultural Sciences
    • View Item
    •   NWU-IR Home
    • Research Output
    • Faculty of Natural and Agricultural Sciences
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Normality of spaces of operators and quasi-lattices

    Thumbnail
    Date
    2015
    Author
    Messerschmidt, Miek
    Metadata
    Show full item record
    Abstract
    We give an overview of normality and conormality properties of pre-ordered Banach spaces. For pre-ordered Banach spaces X and Y with closed cones we investigate normality of B(X,Y) in terms of normality and conormality of the underlying spaces X and Y. Furthermore, we define a class of ordered Banach spaces called quasi-lattices which strictly contains the Banach lattices, and we prove that every strictly convex reflexive ordered Banach space with a closed proper generating cone is a quasi-lattice. These spaces provide a large class of examples X and Y that are not Banach lattices, but for which B(X,Y) is normal. In particular, we show that a Hilbert space H endowed with a Lorentz cone is a quasi-lattice (that is not a Banach lattice if dimH≥3), and satisfies an identity analogous to the elementary Banach lattice identity ∥|x|∥=∥x∥ which holds for all elements x of a Ba
    URI
    http://hdl.handle.net/10394/18550
    http://dx.doi.org/10.1007/s11117-015-0323-y
    http://link.springer.com/article/10.1007/s11117-015-0323-y
    Collections
    • Faculty of Natural and Agricultural Sciences [4855]

    Copyright © North-West University
    Contact Us | Send Feedback
    Theme by 
    Atmire NV
     

     

    Browse

    All of NWU-IR Communities & CollectionsBy Issue DateAuthorsTitlesSubjectsAdvisor/SupervisorThesis TypeThis CollectionBy Issue DateAuthorsTitlesSubjectsAdvisor/SupervisorThesis Type

    My Account

    LoginRegister

    Copyright © North-West University
    Contact Us | Send Feedback
    Theme by 
    Atmire NV