A Note on the Order Lozanovsky Spectrum for Positive Operators

On the Point Spectrum of Positive Operators

1. Recently, G.-C. Rota proved the following result: Let (S, 2, p) be a measure space of finite measure, P a positive linear operator on Lx(S, 2, u) with Li-norm and L„-norm at most one. If a, | a\ = 1, is an eigenvalue of P such that af=Pf (JELx), then a2 is an eigenvalue such that a2|/|g"=P(|/|g"), where/=|/|g. It can be added that an|/|gn = P(|/|gn) for every integer n; thus Rota proved for ...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

A note on the order graph of a group

 The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.

Note on the spectrum of discrete Schrödinger operators

The spectrum of discrete Schrödinger operator L + V on the d-dimensional lattice is considered, where L denotes the discrete Laplacian and V a delta function with mass at a single point. Eigenvalues of L+V are specified and the absence of singular continuous spectrum is proven. In particular it is shown that an embedded eigenvalue does appear for d ≥ 5 but does not for 1 ≤ d ≤ 4.

A Note on Weighted Composition Operators on L^p-Spaces