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DI Cartwright, HP Lotz (1977)
Disjunkte Folgen in Banachverbänden und Kegel $$p$$ p -absolutsummierende FolgenArch. Math., 28
N Kalton (2003)
Handbook of the Geometry of Banach Spaces
FC Sánchez (2008)
Homomorphisms on Lattices of Continuous FunctionsPositivity., 12
Ordered vector spaces E and F are said to be order isomorphic if there is a (not necessarily linear) bijection $$T: E\rightarrow F$$ T : E → F such that $$x\ge y$$ x ≥ y if and only if $$Tx \ge Ty$$ T x ≥ T y for all $$x,y \in E$$ x , y ∈ E . We investigate some situations under which an order isomorphism between two Banach lattices implies the persistence of some linear lattice structure. For instance, it is shown that if a Banach lattice E is order isomorphic to C(K) for some compact Hausdorff space K, then E is (linearly) isomorphic to C(K) as a Banach lattice. Similar results hold for Banach lattices order isomorphic to $$c_{0}$$ c 0 , and for Banach lattices that contain a closed sublattice order isomorphic to $$c_{0}$$ c 0 .
Positivity – Springer Journals
Published: Nov 9, 2015
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