Some estimates on entropy numbers

First we show that the Carl-Maurey inequality for entropy numbers

An inequality between thep- and (p, 1)-summing norm of finite rank operators fromC(K)-spaces

We show, for any operatorT from aC(K)-space into a Banach space with rank (T)≤n, the inequality , whereC≤4.671 is a numerical constant. The factor (1+logn)^1−1/p is asymptotically correct. This inequality extends a result of Jameson top ≠ 2. Several applications are given — one is a positive solution of a conjecture of Rosenthal and Szarek: For 1≤p<q<2,      

Optimal comparison of the <Emphasis Type="Italic">p</Emphasis>-norms of Dirichlet polynomials

In this sequel to Part I of this series [8], we present a different approach to bounding the expected number of real zeroes of random polynomials with real independent identically distributed coefficients or more generally, exchangeable coefficients. We show that the mean number of real zeroes does not grow faster than the logarithm of the degree. The main ingredients of our approach are Descartes’ rule of signs and a new anti-concentration inequality for the symmetric group. This paper can be read independently of part I in this series.     

Orlicz norm estimates for eigenvalues of matrices

Let φ be a supermultiplicative Orlicz function such that the function $t \mapsto \varphi \left( {\sqrt t } \right)$ is equivalent to a convex function. Then each complexn×n matrixT=(τ _ij ) _{i, j} satisfies the following eigenvalue estimate: $\left\| {\left( {\lambda _i \left( T \right)} \right)_{i = 1}^n } \right\|_{\ell _\varphi } \leqslant C\left\| ( \right\|\left( {\tau _{ij} } \right)_{i = 1}^n \left\| {_{_{\ell _{\varphi *} } } )_{j = 1}^n } \right\|\ell _{\bar \varphi } $ . Here, ?_* stands for Young’s conjugate function of φ, ?, $\bar \varphi $ is the minimal submultiplicative function dominating φ andC>0 a constant depending only on φ. For the power function φ(t)=t ^p ,p≥2 this is a celebrated result of Johnson, König, Maurey and Retherford from 1979. In this paper we prove the above result within a more general theory of related estimates.     

An Elementary Approach to an Eigenvalue Estimate for Matrices

A celebrated result of Johnson, Maurey, König and Retherford from 1977 states that for every complex matrix satisfies the following eigenvalue estimate:

Polynomials in operator space theory

The aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces. For this purpose we take advantage of the basic fact that the space P^m(E)$P^m(E)$ of all m-homogeneous polynomials on a vector space E can be identified with the algebraic dual of the m  -th symmetric tensor product ⊗^m,sE${\otimes }^{m,s}E$. Given an operator space V, we study several different types of completely bounded polynomials on V   which form the operator space duals of ⊗^m,sV${\otimes }^{m,s}V$ endowed with related operator structures. Of special interest are what we call Haagerup, Kronecker, and Schur polynomials – polynomials associated with different types of matrix products.     

A study of resveratrol-copper complexes by electrospray ionization mass spectrometry and density functional theory calculations

Resveratrol is a polyphenolic compound found in plants and human foods which has shown biological activities including chemoprevention, acting through a mechanism which involves the reduction of Cu(II) species. By electrospray ionization (ESI) mass spectrometry we have produced and detected the resveratrol-copper complexes [Resv+Cu](+), [Resv+Cu+H(2)O](+) and [2Resv+Cu](+) by using a resveratrol/CuSO(4) solution in CH(3)CN/H(2)O. The most stable structures of the detected complexes have been calculated at the B3LYP/6-311G(d) level of theory. Resveratrol interacts with the copper ion through nucleophilic carbon atoms on the aromatic ring and the alkenyl group. The fact that only singly charged ions were observed implies that Cu(II) is reduced to Cu(I) in the ESI process. For investigating the structure-reactivity correlation, we have carried out a similar study on the synthetic analogue dihydroresveratrol (DHResv). For the latter only the [DHResv+Cu](+) complex has been detected.     

$$\pmb {{\mathcal {H}}_{p}}$$Hp-Theory of General Dirichlet Series

Journal of Fourier Analysis and Applications - Inspired by results of Bayart on ordinary Dirichlet series $$\sum a_n n^{-s}$$, the main purpose of this article is to start an $${\mathcal...