dc.contributor.author Messerschmidt, Miek dc.date.accessioned 2016-09-06T08:37:48Z dc.date.available 2016-09-06T08:37:48Z dc.date.issued 2015 dc.identifier.citation Messerschmidt, M. 2015. Normality of spaces of operators and quasi-lattices. Positivity,19(4):695-724. [http://link.springer.com/journal/11117] en_US dc.identifier.issn 1385-1292 dc.identifier.issn 1572-9281 (Online) dc.identifier.uri http://hdl.handle.net/10394/18550 dc.identifier.uri http://dx.doi.org/10.1007/s11117-015-0323-y dc.identifier.uri http://link.springer.com/article/10.1007/s11117-015-0323-y dc.description.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 en_US dc.language.iso en en_US dc.publisher Springer en_US dc.subject (Pre)-ordered Banach space en_US dc.subject operator norm en_US dc.subject quasi-lattice en_US dc.subject normality en_US dc.subject conormality en_US dc.subject Lorentz cone en_US dc.title Normality of spaces of operators and quasi-lattices en_US dc.type Article en_US dc.contributor.researchID 25788639 - Messerschmidt, Hendrik Jacobus Michiel
﻿

Files in this item

FilesSizeFormatView

There are no files associated with this item.

Theme by