Bernstein–Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds

Bernstein–Nikolskii inequalities and Riesz interpolation formula are established for eigenfunctions of Laplace operators and polynomials on compact homogeneous manifolds.     

Compact quantum ergodic systems

We develop theory of multiplicity maps for compact quantum groups. As an application, we obtain a complete classification of right coideal C^∗-algebras of C(SUq(2)) for q∈[−1,1)?{0}. They are labeled with Dynkin diagrams, but classification results for positive and negative cases of q are different. Many of the coideals are quantum spheres or quotient spaces by quantum subgroups, but we do have other ones in our classification list.     

Design of a PXR experiment based on the NCEL

Parametric X-ray Radiation (PXR) can be used as a novel, quasi-monochromatic energy-tunable and high-yield X-ray source. It is produced at the Bragg angle by a relativistic electron beam passing through the periodic structure of crystal materials. This article concerns the PXR experiment using low energy electrons (10 MeV) from NCEL (Novel Compact Electron-Linac). The difficulty of the experiment is to distinguish the PXR photons form the background. The design of the experiment relies mainly on the yield of PXR, the Bremsstrahlung background of the X-rays and the capability of the detector.     

连续信息代数

给出基于自由域信息代数和带论域信息代数上的连续性概念.证明在城集格有最大元的情况下,两种连续性之间是相互对应的.定义了连续信息代数之间的连续映射的概念,证得:若(φ,D),(ψ,E)都是强连续的信息代数.则([φ→ψ]c,D×E)也是强连续的.     

Some quasinilpotent generators of the hyperfinite II1 factor

For each sequence n{cn} in l₁(N) we define an operator A in the hyperfinite II₁-factor R. We prove that these operators are quasinilpotent and they generate the whole hyperfinite II₁-factor. We show that they have non-trivial, closed, invariant subspaces affiliated to the von Neumann algebra and we provide enough evidence to suggest that these operators are interesting for the hyperinvariant subspace problem. We also present some of their properties. In particular, we show that the real and imaginary part of A are equally distributed, and we find a combinatorial formula as well as an analytical way to compute their moments. We present a combinatorial way of computing the moments of A^∗A.     

Norm inequalities in operator ideals

In this paper we introduce a new technique for proving norm inequalities in operator ideals with a unitarily invariant norm. Among the well-known inequalities which can be proved with this technique are the Löwner-Heinz inequality, inequalities relating various operator means and the Corach-Porta-Recht inequality. We prove two general inequalities and from them we derive several inequalities by specialization, many of them new. We also show how some inequalities, known to be valid for matrices or bounded operators, can be extended with this technique to normed ideals in C^∗-algebras, in particular to the noncommutative Lp-spaces of a semi-finite von Neumann algebra.     

Approximating composition operator norms on the Dirichlet space

Let φ be any univalent self-map of the unit disk D whose image Ω≡φ(D) is compactly contained in D. We provide a method for approximating the norm of the composition operator Cφ on the Dirichlet space to any desired degree of accuracy. The approximation uses a special basis which is orthogonal in both the Bergman space on the disk and the Bergman space on Ω.     

An application of Ekeland's Variational Principle to the spectrum of nonlinear homogeneous gradient operators

The Ekeland Variational Principle is used to prove the nonemptiness of the spectrum for positively homogeneous gradient mappings in Hilbert space. Under additional information on the measure of noncompactness of the operator, this leads to the existence of a maximal (or minimal) compact eigenvalue for the operator itself.     

An addendum to the multiplication and factorization theorems of brodskiǐ—livšic—potapov

In this paper the classical Brodskiǐ—Liv?ic— operator colligation is generalized to certain pairs of bounded linear operators and the corresponding characteristic operator—valued (transfer) function is introduced. The fundamental results due to M.S. Brodskiǐ, M.S. Liv?ic, and V.P. Potapov are then extended to such colligations. These new types of colligations can be used to obtain, for instance, realization results for general Herglotz—Nevanlinna functions.     

How to distinguish quantum covariances using uncertainty relations

To each operator monotone function it is possible to associate a quantum version of the classical covariance. We show that: i) only for regular quantum covariances one can prove non-trivial uncertainty relations; ii) the usual quantum covariance gives the best inequalities in this setting.