A compactness criterion for Stieltjes transformation S λ : L 2 → L 2 of the form (1.1) is obtained. The main result is conditions for belonging S λ to Schatten-von Neumann class S p , 0 < p < ∞.

Schatten-IT sind Systeme, Organisationsstrukturen oder Prozesse, die Geschäftsprozesse unterstützen, aber weder technisch noch strategisch ins IT-Service-Management integriert sind. Um in Unternehmen ein Bewusstsein für Schatten-IT zu schaffen, wurde ein Lernspiel entwickelt, welches die Facetten von Schatten-IT spielerisch verdeutlichen soll. In diesem Paper wird der Prototyp dieses Spieles vo...

We apply the complex interpolation method to prove that, given two spacesB p0,a;s0 , B (n) p1,b;s1 of n-tuples of operators in the p-Schatten class of a Hilbert space H , endowed with weighted norms associated to positive and invertible operators a and b of B(H) then, the curve of interpolation (B p0,a;s0 , B (n) p1,b;s1 )[t] of the pair is given by the space of n-tuples of operators in the pt-...

They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius we develop diverse inequalities involving w_N. also particular cases a fixed N(.), for instance p-Schatten norms. In [A generalization radius. Linear Algebra Appl. 569 (2019)], Abu Omar Kittaneh defined new That is, given norm $N(\cdot)$ on $\bh$, space bounded linear...

Abstract. There are well-known relationships between compressed sensing and the geometry of the finite-dimensional lp spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via l1minimization in terms of the Gelfand widths of certain identity mappings between finitedimensional l1 and l2 spaces, whereas a more recen...

Sketching is a prominent algorithmic tool for processinglarge data. In this paper, we study the problem of sketchingmatrix norms. We consider two sketching models. The firstis bilinear sketching, in which there is a distribution overpairs of r×n matrices S and n× s matrices T such that forany fixed n×n matrix A, from S ·A ·T one can approximate‖A‖p up to an approxima...

In this paper we analyse optimality of the stable fixed point of the double bracket equations. We introduce different types of optimality and prove local and global optimality results with respect to the Schatten p-norms.

In current molecular biology, it becomes more and more important to identify differentially expressed genes closely correlated with a key biological process from gene expression data. In this paper, based on the Schatten p-norm and Lp-norm, a novel p-norm robust feature extraction method is proposed to identify the differentially expressed genes. In our method, the Schatten p-norm is used as th...

Given an n×d matrix A, its Schatten-p norm, p ≥ 1, is defined as ‖A‖p = (∑rank(A) i=1 σi(A) p )1/p , where σi(A) is the i-th largest singular value of A. These norms have been studied in functional analysis in the context of non-commutative `p-spaces, and recently in data stream and linear sketching models of computation. Basic questions on the relations between these norms, such as their embed...

Namita Das P. G. Department of Mathematics, Utkal University, Vanivihar, Bhubaneswar, Orissa 751004, India Correspondence should be addressed to Namita Das, [email protected] Received 23 July 2009; Revised 7 September 2009; Accepted 14 October 2009 Recommended by Palle Jorgensen We have shown that if the Toeplitz operator Tφ on the Bergman space La D belongs to the Schatten class Sp, 1 ≤...