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Monotonic norms in ordered Banach spaces

Part of: Topological linear spaces and related structures Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

K. F. Ng  and
C. K. Law
K. F. Ng
Affiliation:
Department of Mathematics, The Chinese University of Hong KongHong Kong
C. K. Law
Affiliation:
Department of Mathematics, The Chinese University of Hong KongHong Kong
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Abstract

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Let 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*.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices 46B10: Duality and reflexivity

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 217 - 219
Copyright
Copyright © Australian Mathematical Society 1988

References

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