Regularly ordered Banach spaces and positively convex spaces

1984 ◽  
Vol 7 (1) ◽  
pp. 84-112 ◽  
Author(s):  
Dieter Pumplün
Author(s):  
K. F. Ng ◽  
C. K. Law

AbstractLet B be an ordered Banach space with ordered Banach dual space. Let N denote the canonical half-norm. We give an alternative proof of the following theorem of Robinson and Yamamuro: the norm on B is α-monotone (α ≥ 1) if and only if for each f in B* there exists g ∈ B* with g ≥ 0, f and ∥g∥ ≤ α N(f). We also establish a dual result characterizing α-monotonicity of B*.


2012 ◽  
Vol 142 (5) ◽  
pp. 1043-1050 ◽  
Author(s):  
Daniel Franco ◽  
Gennaro Infante ◽  
Juan Perán

We provide new sufficient conditions for the existence of multiple fixed points for a map between ordered Banach spaces. An interesting feature of this approach is that we require conditions not on two boundaries, but rather on one boundary and a point with some extra information on the monotonicity of the nonlinearity on a certain set. We apply our results to prove the existence of at least two positive solutions for a nonlinear boundary-value problem that models a thermostat.


1984 ◽  
Vol 30 (3) ◽  
pp. 357-380 ◽  
Author(s):  
Sadayuki Yamamuro

In a Banach lattice or the hermitian part of a C*-algebra, every element a admits a decomposition a = a+ − a− such that and N(−a) = ‖a−‖, where N is the canonical half-norm of the positive cones. In general ordered Banach spaces, this property is related to the order structure of the duality map and the metric projectability of the positive cones, and it turns out to be equivalent to an “orthogonal” decomposability.


1987 ◽  
Vol 30 (3) ◽  
pp. 397-400 ◽  
Author(s):  
Ioannis A. Polyrakis

In this paper we study the existence of strongly exposed points in unbounded closed and convex subsets of the positive cone of ordered Banach spaces and we prove the following characterization for the space l1(Γ): A Banach lattice X is order-isomorphic to l1(Γ) iff X has the Schur property and X* has quasi-interior positive elements.


1978 ◽  
Vol s2-17 (1) ◽  
pp. 107-109
Author(s):  
M. N. Chaudhary ◽  
H. R. Atkinson

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