Open AccessA remark to a theorem of Yu. A. Abramovich
Author(s) -
Eduard Emelyanov
Publication year - 2003
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-03-07111-9
Subject(s) - mathematics , bounded function , surjective function , isometry (riemannian geometry) , pure mathematics , bounded inverse theorem , discrete mathematics , banach space , mathematical analysis , bounded operator
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.