PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.3, pp.781-782, 2004 (Journal Indexed in SCI)
Article / Article
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
positive isometry, doubly power bounded operator, renorming problem
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.