A remark to a theorem of Yu. A. Abramovich
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.3, pp.781-782, 2004 (SCI-Expanded, Scopus)
- 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
- Open Archive Collection: AVESIS Open Access Collection
- 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.