A remark to a theorem of Yu. A. Abramovich
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- by Eduard Yu. Emel’yanov PDF
- Proc. Amer. Math. Soc. 132 (2004), 781-782 Request permission
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
- Yu. A. Abramovich, Isometries of normed lattices, Optimizatsiya 43(60) (1988), 74–80 (Russian). MR 1007934
- John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 105017, DOI 10.2140/pjm.1958.8.459
Additional Information
- Eduard Yu. Emel’yanov
- Affiliation: Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia
- MR Author ID: 353198
- Email: emelanov@math.nsc.ru
- 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
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 781-782
- MSC (2000): Primary 47B65, 46B03, 46B42
- DOI: https://doi.org/10.1090/S0002-9939-03-07111-9
- MathSciNet review: 2019955