Abstract
LetEbe a Banach Lattice. We will considerEto be weakly sequentially complete and to have a weak unitu. Thus we may representEas a lattice of real valued functions defined on a measure space (χ,,μ). There is a setR⊂χsuch thatRsupports a maximal invariant functionΦfor a postive contractionTonE[5]. LetN=χ—Rbe the complement ofR. Akcoglu and Sucheston showed thatwhereE+is the positive cone ofE. If in addition a monotone condition (UMB) is satisfied, then the same authors showed [4] thatconverges in norm.
Publisher
Canadian Mathematical Society