Regularly ordered Banach spaces and positively convex spaces

1984 ◽  
Vol 7 (1) ◽  
pp. 84-112 ◽  
Author(s):  
Dieter Pumplün
Keyword(s):  
Banach Spaces ◽  
Ordered Banach Spaces ◽  
Convex Spaces

scholarly journals Monotonic norms in ordered Banach spaces

1988 ◽  
Vol 45 (2) ◽  
pp. 217-219 ◽  
Author(s):  
K. F. Ng ◽  
C. K. Law
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Dual Space ◽  
Alternative Proof ◽  
Ordered Banach Space ◽  
Dual Result ◽  
Ordered Banach Spaces

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*.

A new criterion for the existence of multiple solutions in cones

2012 ◽  
Vol 142 (5) ◽  
pp. 1043-1050 ◽  
Author(s):  
Daniel Franco ◽  
Gennaro Infante ◽  
Juan Perán
Keyword(s):  
Boundary Value Problem ◽  
Fixed Points ◽  
Banach Spaces ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Extra Information ◽  
New Criterion ◽  
Multiple Fixed Points ◽  
Ordered Banach Spaces

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.

scholarly journals On orthogonally decomposable ordered Banach spaces

1984 ◽  
Vol 30 (3) ◽  
pp. 357-380 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Order Structure ◽  
Duality Map ◽  
Ordered Banach Spaces

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.

scholarly journals Strongly exposed points and a characterization of l1 (Γ) by the Schur property

1987 ◽  
Vol 30 (3) ◽  
pp. 397-400 ◽  
Author(s):  
Ioannis A. Polyrakis
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Positive Cone ◽  
Schur Property ◽  
Positive Elements ◽  
Strongly Exposed Points ◽  
Ordered Banach Spaces ◽  
Convex Subsets ◽  
Quasi Interior

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.

Ordered Banach Spaces with Compact Order Intervals

1978 ◽  
Vol s2-17 (1) ◽  
pp. 107-109
Author(s):  
M. N. Chaudhary ◽  
H. R. Atkinson
Keyword(s):  
Banach Spaces ◽  
Order Intervals ◽  
Ordered Banach Spaces
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