J Austral Math Soc Ser A 45 pp217--219, 1988.

Monotonic Norms in Ordered Banach Spaces

K. F. Ng and C. K. Law

Abstract

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 a-monotone (a ³ 1) if and only if for each f in B* there exists g Î B* with g ³ 0, f and ||g|| £ aN(f). We also establish a dual result characterizing a-monotonicity of B*.

1980 AMS Subject Classification: 46A40, 46B10

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Authors

K. F. Ng

C. K. Law

Department of Mathematics, The Chinese University of Hong Kong, Hong Kong.