Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...

We consider the Renormalization-Group coupled equations for the effective potential V (φ) and the field strength Z(φ) in the spontaneously broken phase as a function of the infrared cutoff momentum k. In the k → 0 limit, the numerical solution of the coupled equations, while reproducing the well-known convexity property of V (φ), indicates a sharp peaking of Z(φ) close to the end points of the ...

Let B be a generator of positivity preserving (shortly, positive) semi-group in L 2 on a space with-nite measure. It is supposed that the semigroup e ?tB ; t > 0; acts continuously from L 2 to L 1. For a measurable function V 0 an estimate for the number of negative eigenvalues of the operator B ? V is obtained, generalizing the similar estimate for the the Schrr odinger operator (the CLR-estim...