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Addition of an identity to an ordered Banach space

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

Derek W. Robinson  and
Sadayuki Yamamuro
Derek W. Robinson
Affiliation:
Department of MathematicsInstitute of Advanced Studies The Australian National UniversityP.O. Box 4Canberra, A.C.T. 2600, Australia
Sadayuki Yamamuro
Affiliation:
Department of MathematicsInstitute of Advanced Studies The Australian National UniversityP.O. Box 4Canberra, A.C.T. 2600, Australia
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Abstract

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Given an ordered Banach space ℬ equipped with an order-norm we construct a larger space ℬ¯ with an order-norm and order-identity such that B is isometrically order-isomorphic to a Banach subspace of B. We also discuss the extension of positive operators from ℬto ℬ¯.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 200 - 210
Copyright
Copyright © Australian Mathematical Society 1983

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