We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class p...

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.

The first main result in this article provides an error bound for balanced truncation where the matrix norm used is a general Schatten norm rather than the usual operator norm. The second main result in this article is that for the Schatten 1-norm (the trace class norm) this bound, for systems with a semi-definite Hankel operator, is in fact an equality. This class of systems for which we obtai...

The famous Dantzig estimator(DE) has been applied in quantum state tomography for estimating an unknown low rank density matrix. The density matrices are positively semi-definite Hermitian matrices with unit trace that describe the states of quantum systems. The main contribution of this paper is deriving the low rank oracle inequality of DE and proving its convergence rates in the Schatten p-n...

A countable discrete group is said to be Frobenius stable if every function from the unitary matrices that “almost multiplicative” in norm “close” a representation norm. The purpose of this paper show finitely generated nilpotent groups are not virtually cyclic stable. Our argument proves same result for other unnormalized Schatten p-norms with 1<p≤∞.

We study a new class of structured Schatten norms for tensors that includes two recently proposed norms (“overlapped” and “latent”) for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we analyze the performance of “latent” approach for tensor decomposition, which was empirically found to perform better than the “overlapped” approach in s...

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...