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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A remark to a theorem of Yu. A. Abramovich


Author: Eduard Yu. Emel'yanov
Journal: Proc. Amer. Math. Soc. 132 (2004), 781-782
MSC (2000): Primary 47B65, 46B03, 46B42
Published electronically: October 2, 2003
MathSciNet review: 2019955
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Abstract: A remarkable theorem due to Abramovich (1988) states that any surjective positive isometry on a Banach lattice has a positive inverse. In this note we discuss a renorming problem for Banach lattices and show that the theorem cannot be generalized to the case of the doubly power bounded positive operators.


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Additional Information

Eduard Yu. Emel'yanov
Affiliation: Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia
Email: emelanov@math.nsc.ru

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07111-9
PII: S 0002-9939(03)07111-9
Keywords: Positive isometry, doubly power bounded operator, renorming problem
Received by editor(s): June 19, 2002
Received by editor(s) in revised form: October 25, 2002
Published electronically: October 2, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society