A remark to a theorem of Yu. A. Abramovich

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Emel'yanov E.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.3, pp.781-782, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 132 Issue: 3
  • Publication Date: 2004
  • Doi Number: 10.1090/s0002-9939-03-07111-9
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.781-782
  • Keywords: positive isometry, doubly power bounded operator, renorming problem
  • Middle East Technical University Affiliated: Yes

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.