Some Convexity Results for Algebras

On the Diagonals of Projections in Matrix Algebras Over Von Neumann Algebras

ON THE DIAGONALS OF PROJECTIONS IN MATRIX ALGEBRAS OVER VON NEUMANN ALGEBRAS Soumyashant Nayak Richard V. Kadison The main focus of this dissertation is on exploring methods to characterize the diagonals of projections in matrix algebras over von Neumann algebras. This may be viewed as a non-commutative version of the generalized Pythagorean theorem and its converse (Carpenter’s Theorem) studie...

A Noncommutative Convexity in C ∗ - Bimodules

Let A and B be C∗-algebras. We consider a noncommutative convexity in Hilbert A -B-bimodules, called A -B-convexity, as a generalization of C∗-convexity in C∗-algebras. We show that if X is a Hilbert A -B-bimodule, then Mn(X ) is a Hilbert Mn(A )-Mn(B)-bimodule and apply it to show that the closed unit ball of every Hilbert A -B-bimodule is A -B-convex. Some properties of this kind of convexity...

Fundamental results for pointfree convex geometry

Inspired by locale theory, we propose “pointfree convex geometry.” We introduce the notion of convexity algebra as pointfree convexity space. There are two notions of point for convexity algebra: one is chain-prime meet-complete filter and the other is maximal meet-complete filter. In this paper we show the following: (1) the former notion of point induces a dual equivalence between the categor...

General Convexity of Some Functionals in Seminormed Spaces and Seminormed Algebras

SOME PROPERTIES FOR FUZZY CHANCE CONSTRAINED PROGRAMMING

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

New Results on Ideals in $MV$-‎algebras‎

In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...