On New Majorization Theorems

Some new localization theorems on Hamiltonian properties

Let G be a 2-connected graph with n ?: 3 vertices such that for any two vertices u, v at distance two in an induced subgraph K 1,3 or P4 of G, the inequality d(u) + d(v) ?: IN(u) U N(v) U N(w)ls holds for all w E N(u) n N(v). We prove that (i) if s = 1 and IN(u) n N(v)1 ?: 2, then G is hamiltonian or K p,p+1 ~ G ~ Kp + K p+1; (ii) if s = 0, then G is either pancyclic, or bipartite graph. This g...

Non-commutative Schur-horn Theorems and Extended Majorization for Hermitian Matrices

Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n × n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give an spectral characterization of the set EA(Un(B)) = {EA(U B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit...

On properties of the generalized majorization

On Majorization, Favard and Berwald Inequalities

In this paper, we obtain extensions of majorization type results and extensions of weighted Favard’s and Berwald’s inequality. We prove positive semi-definiteness of matrices generated by differences deduced from majorization type results and differences deduced from weighted Favard’s and Berwald’s inequality. This implies a surprising property of exponentially convexity and log-convexity of th...

Ela on Properties of the Generalized Majorization

Abstract. In this paper, a complete solution of a problem involving generalized majorization of partitions is given: for two pairs of partitions (d, a) and (c,b) necessary and sufficient conditions for the existence of a partition g that is majorized by both pairs is determined. The obtained conditions are explicit, the solution is constructive and it uses novel techniques and indices. Although...