It is shown that every locally idempotent (locally m-PSEUDOCONVEX)Hausdorff algebra A with PSEUDOCONVEX VON NEUMANN BORNOLOGY is a regular (respectively, bornological) inductive limit of metrizable locally m-(kB-convex) subalgebras AB of A. In the case where A, in addition, is sequentially BA-complete (sequentially advertibly complete), then every subalgebraAB is a locally m-(kB-convex) Frechet algebra (respectively, an advertibly complete metrizable locally m-(kB-convex) algebra) for some kB Î (0, 1]. Moreover, for a commutative unital locally m-PSEUDOCONVEX Hausdorff algebra A over C with PSEUDOCONVEX VON NEUMANN BORNOLOGY, which at the same time is sequentially BA-complete and advertibly complete, the statements (a)–(j) of Proposition 3.2 are equivalent.

We show that a regular VON NEUMANN Q-m-convex Fréchet algebra is of finite dimension. We also show that a regular VON NEUMANN m-convex Fréchet algebra is a projective limit of finite dimensional algebras. Finally, we prove that a bilateral Q-F-algebra is a regular VON NEUMANN algebra if and only if it is isomorphic to a finite product of algebras which are also fields.

Please click on PDF to view the abstract

Let M be a factor VON NEUMANN algebra. It is shown that every nonlinear *-Lie higher derivation D={Æn}nÎN on M is additive. In particular, if M is infinite type I factor, a concrete characterization of D is given.

In this article we study topological VON NEUMANN regularity and principal VON NEUMANN regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras with some other known Banach algebras and with each other. In particular we show that the class of topologically VON NEUMANN regular Banach algebras contains all C*-algebras, group algebras of compact abelian groups and certain weakly amenable Banach algebras while it excludes measure algebras of certain locally compact Abelian groups. Moreover we show that in a unital amenable Banach algebra principal regularity implies topological regularity. Finally we use topological regularity to obtain some information about hereditary C*-subalgebras of a given C*-algebra.

Please click on PDF to view the abstract