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A remark to a theorem of Yu. A. Abramovich

Author(s): Eduard Yu. Emel'yanov
Journal: Proc. Amer. Math. Soc. 132 (2004), 781-782.
MSC (2000): Primary 47B65, 46B03, 46B42
Posted: October 2, 2003
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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.

References:

[1]: Yu. A. Abramovich, Isometries of normed lattices, (Russian), Optimizatsiya 43(60) (1988), 74-80. MR 90k:46042
[2]: J. Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459-466. MR 21:3764

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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: 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
Posted: October 2, 2003
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2003, American Mathematical Society


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