Abstract We prove a very general fixed point theorem in the space of functions taking values random normed (RN-space). Next, we show several its consequences and, among others, present applications it proving Ulam stability results for inhomogeneous linear functional equation with variables class f mapping vector X into an RN-space. Particular cases are instance equations Cauchy, Jensen, Jordan...

It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its pr...

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group Fr, 2 ≤ r ≤ ∞, on a probability ...

It is shown that every locally idempotent (locallym-pseudoconvex) Hausdorff algebra A with pseudoconvex vonNeumannbornology is a regular (respectively, bornological) inductive limit of metrizable locallym-(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) Fréchet al...

Es wird ein inkrementeller Ansatz zur Koreferenzanalyse deutscher Texte vorgestellt. Wir zeigen anhand einer breiten empirischen Untersuchung, dass ein inkrementelles Verfahren einem nichtinkrementellen überlegen ist und dass jeweils die Verwendung von mehreren Klassifizierern bessere Resultate ergibt als die Verwendung von nur einem. Zudem definieren wir ein einfaches Salienzmass, dass annäher...

1. Introduction. Let 5 be a measure space with a countably additive , (T-finite, complete (non-negative) measure. J. von Neumann has proved that, from each class x of measurable sets modulo null sets of 5, a representative set R(x)Ex can be picked in such a way

Given a JBW*-triple Z and a normal contractive projection P : Z −→ Z, we show that the (Murray-von Neumann) type of each summand of P (Z) is dominated by the type of Z.

We show that the following five categories are equivalent: (1) opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) locales; (4) hyperstonean (5) spaces. This result can be seen as a measure-theoretic counterpart Gelfand duality between unital C*-algebras and Hausdorff topological

In this article, we proved the following results. Let L(F (ni)) be the free group factor on ni generators and λ(gi) be one of standard generators of L(F (ni)) for 1 ≤ i ≤ N . Let Ai be the abelian von Neumann subalgebra of L(F (ni)) generated by λ(gi). Then the abelian von Neumann subalgebra ⊗i=1Ai is a maximal injective von Neumann subalgebra of ⊗i=1L(F (ni)). When N is equal to infinity, we o...