Equivalent conditions are obtained for weak convergence of iterates of positive contractions in theL1-spaces for general von Neumann algebra and generalJBWalgebras, as well as for Segal-DixmierLp-spaces(1≤p<∞)affiliated to semifinite von Neumann algebras and semifiniteJBWalgebras without direct summands of typeI2.
We introduce and study locally AW * -algebras (Baer locally C *algebras) as a locally multiplicatively convex generalization of AW * -algebras of Kaplansky. Among other basic properties of these algebras, it is established that:• A locally C * -algebra is a locally AW * -algebra iff there exists its Arens-Michael decomposition consisting entirely of AW * -algebras;• A bounded part of a locally AW * -algebra is an AW * -algebra;• The Spectral Theorem for locally AW * -algebras.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.