‎let $lambda_1,dots,lambda_n$ be positive real numbers such that‎‎$sum_{k=1}^n lambda_k=1$‎. ‎we prove that for‎‎any positive operators $a_1,a_2,cdots‎, ‎a_n$ in semifinite von‎‎neumann algebra $m$ with faithful normal trace that $t(1)

‎Let $lambda_1,dots,lambda_n$  be positive real numbers such that $sum_{k=1}^n lambda_k=1$. In this paper, we prove that for any positive operators $a_1,a_2,ldots, a_n$ in semifinite von Neumann algebra $M$ with faithful normal trace that $t(1)

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.

Meilijson and Nadas [1979] have obtained stochastic bounds in the convex majorisation sense to the critical path length of a project network with random activity durations. In this paper we present those results in a more general framework and, using similar techniques, obtain bounds for shortest route, maximal flow and reliability system lifetime. Subject classification: #488 Bounds for stocha...

We extend the results of Mary Embry [9] on majorisation and range inclusion of bounded linear operators on Banach spaces to the case when one of the two operators is a convex process. An application in controllability is given.

The polynomial matrix EVD (PEVD) is an extension of the conventional eigenvalue decomposition (EVD) to polynomial matrices. The purpose of this article is to provide a review of the theoretical foundations of the PEVD and to highlight practical applications in the area of broadband blind source separation (BSS). Based on basic definitions of polynomial matrix terminology such as parahermitian a...

We develop majorisation results that characterise changes in eigenvector components of a graph’s adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for singleand multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dom...