Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-16T21:15:15.339Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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

[1]Arendt, W., Chernoff, P. R. and Kato, T., ‘A generalization of dissipativity and positive semigroups’, J. Operator Theory 8 (1982), 167–180.Google Scholar
[2]Ng, K. F., ‘The duality of partially ordered Banach spaces’, Proc. London Math. Soc. 19 (1969), 269–288.CrossRefGoogle Scholar
[3]Ng, K. F., ‘A note on partially ordered Banach spaces’, J. London Math. Soc. (2) 1 (1969), 520–524.CrossRefGoogle Scholar
[4]Wong, Y. C. and Ng, K. F., Partially ordered topological vector spaces, (Clarendon Press, Oxford, 1973).Google Scholar
[5]Robinson, D. W. and Yamamuro, S., ‘The Jordan decomposition and half-norms’, Pacific J. Math. 110 (1984), 345–353.CrossRefGoogle Scholar
[6]Robinson, D. W. and Yamamuro, S., ‘The canonical half-norm, dual half-norms and monotonic norms’, Tôhoku Math. J. 35 (1983), 375–386.CrossRefGoogle Scholar