We consider the properties of the Shannon entropy for two probability distributions which stand in the relationship of majorization. Then we give a generalization of a theorem due to Uhlmann, extending it to infinite dimensional Hilbert spaces. Finally we show that for any quantum channel Φ, one has S(Φ(ρ)) = S(ρ) for all quantum states ρ if and only if there exists an isometric operator V such...

and Applied Analysis 3 where dV z is the Lebesgue volume measure on B. Some facts on mixed-norm spaces in various domains in C can be found, for example, in 6–8 see also the references therein . For 0 < p < ∞ the Hardy space H B H consists of all f ∈ H B such that ∥ ∥f ∥ ∥ Hp : sup 0<r<1 (∫ ∂B ∣ ∣f rζ ∣ ∣dσ ζ )1/p < ∞. 1.10 For p 2 the Hardy and the weighted Bergman space are Hilbert. Let φ be ...

1. THE PROBLEM On a square lattice (we consider here a D=2+1 lattice for simplicity) the exact rotational symmetry is confined to rotations that are integer multiples of π/2. If we attempt to build operators of spin J from basic components that are identical – that is, related by a lattice symmetry – then there is an ambiguity: exp(iJθ) ≡ exp(iJ ′ θ) ∀θ = nπ 2 (1) if J ′ = J + 4N ∀N (2) Thus, f...

Rigged configurations appear in the Bethe Ansatz study of exactly solvable lattice models as combinatorial objects to index the solutions of the Bethe equations [5, 6]. Based on work by Kerov, Kirillov and Reshetikhin [5, 6], it was shown in [7] that there is a statistic preserving bijection Φ between LittlewoodRichardson tableaux and rigged configurations. The description of the bijection Φ is...

We argue that the dynamic extended molecular orbital (DEMO) method may be less accurate than expected because the motion of the center of mass was not properly removed prior to the SCF calculation. Under such conditions the virial theorem is a misleading indication of the accuracy of the wavefunction. The first step in any quantum–mechanical treatment of atomic and molecular systems is the sepa...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

A holomorphic self-map φ of the unit disk is constructed such that the composition operator induced by φ is bounded on the Hardy-Sobolev space H1 2 of order 2 as well as on the ordinary holomorphic Lipschitz space Lip1 but unbounded on the Zygmund class Λ1. Among these three function spaces we have embedding relations H1 2 ⊂ Lip1 ⊂ Λ1. So, the main points here are that our construction provides...

and Applied Analysis 3 nonexpansive mapping such that F S ∩ A−10/ ∅. Let {xn} be a sequence generated by x0 x ∈ C and un J−1 ( βnJxn ( 1 − βn ) JSJrnxn ) , Cn { z ∈ C : φ z, un ≤ φ z, xn } , Qn {z ∈ C : 〈xn − z, Jx0 − Jxn〉 ≥ 0}, xn 1 ΠCn∩Qnx0 1.6 for all n ∈ N ∪ {0}, where J is the duality mapping on E, {βn} ⊂ 0, 1 , and {rn} ⊂ a,∞ for some a > 0. If lim infn→∞ 1 − βn > 0, then {xn} converges s...

It is known that, due to the fact that L1,∞ not a Banach space, if (Tj)j sequence of bounded operators so thatTj:L1⟶L1,∞, with norm less than or equal ||Tj|| and ∑j||Tj||<∞, nothing can be said about operator T=∑jTj. This origin many difficult open problems. However, we assume thatTj:L1(u)⟶L1,∞(u),∀u∈A1, φ(||u||A1)||Tj||, where φ nondecreasing function A1 Muckenhoupt class weights, then prove e...

In this article we study the action of the Up Hecke operator on the normalized spherical vector φ in the representation of GSp4(Qp) induced from a character on the Borel subgroup. We compute the Petersson norm of Upφ in terms of certain local L-values associated with φ.