The H61der p-norm of an m • n matrix has no explicit representation unless p = 1, 2 or ~ . It is shown here that the p-norm can be estimated reliably in O(mn) operations. A generalization of the power method is used, with a starting vector determined by a technique with a condition est imation flavour. The algor i thm nearly always computes a p-norm estimate correct to the specified accuracy, a...

We introduce and study a class of entanglement criteria based on the idea applying local contractions to an input multipartite state, then computing projective tensor norm output. More precisely, we apply mixed quantum state product from Schatten $$S_1$$ Euclidean space $$\ell _2$$ , which call testers. analyze performance this type bipartite systems, for general pure states, as well some impor...

Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In pa...

Let f be a multiplier for the Drury-Arveson space H n of the unit ball, and let ζ1, ..., ζn denote the coordinate functions. We show that for each 1 ≤ i ≤ n, the commutator [M∗ f ,Mζi ] belongs to the Schatten class Cp, p > 2n. This leads to a localization result for multipliers.

In this supplementary material, we give the detailed proofs of some lemmas, properties and theorems, as well as some additional experimental results on synthetic data and four recommendation system data sets. A More Notations R n denotes the n-dimensional Euclidean space, and the set of all m×n matrices with real entries is denoted by R m×n. Given matrices X and Y ∈ R m×n , the inner product is...

We consider a p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to a linear programming problem with p-order cone constraints. The proposed approach for handling linear programming problems with p-order cone constraints is based on reformulation of p-order cone optimization problems as second order cone programming (SOCP) problems when p...

We consider the class of integral operators Qφ on L (R+) of the form (Qφf)(x) = ∫ ∞ 0 φ(max{x, y})f(y)dy. We discuss necessary and sufficient conditions on φ to insure that Qφ is bounded, compact, or in the Schatten–von Neumann class Sp, 1 < p < ∞. We also give necessary and sufficient conditions for Qφ to be a finite rank operator. However, there is a kind of cut-off at p = 1, and for membersh...

We investigate the connection between the geometry of the image domain of an analytic function mapping the unit disk into itself and the membership of the composition operator induced by this function in the Schatten classes. The purpose is to provide solutions to Lotto’s conjectures and show a new compact composition operator which is not in any of the Schatten classes. 2000 Mathematics Subjec...