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Symmetry groups on ordered Banach spaces

Published online by Cambridge University Press:  17 April 2009

Sadayuki Yamamuro
Sadayuki Yamamuro
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, A.C.T., Australia.
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Abstract

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A symmetry of an ordered Banach space is an order and norm isomorphism which commutes with its ideal centre. A class of ordered Banach spaces is introduced to show that, for a space in this class, the group of symmetries is trivial if and only if the space is lattice-ordered. When this group becomes larger, the space approaches an antilattice. This phenomenon is also investigated.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 177 - 187
Copyright
Copyright © Australian Mathematical Society 1986

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