We establish several deep existence criteria for conditional expectations on von Neumann algebras, and then apply this theory to develop a noncommutative of representing measures characters function algebra. Our main cycle results describes what may be understood as ‘noncommutative Hoffman-Rossi theorem’ giving the weak* continuous measures’ so-called D -characters. These also viewed ‘module’ H...

to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

The purpose of this paper is to describe three techniques that are useful for the investigation of monotone sets and multifunctions, and give two applications of them. The three techniques use the “fg–theorem”, the “big convexification” of a subset of E × E∗ or a multifunction E 7→ 2E (we suppose throughout that E is a nontrivial real Banach space with dual E∗), and the “convex function associa...

Existence of fixed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' fixed point theorem and Walter's theorem. Also, we give an example showing that our main theor...