Spectral sets and operator radii

Stability Radii and Spectral Value Sets for Real Matrix Perturbations

Operator Radii and Unitary Operators

Let ρ ≥ 1 and w ρ (A) be the operator radius of a linear operator A. Suppose m is a positive integer. It is shown that for a given invertible linear operator A acting on a Hilbert space, one has w ρ (A −m) ≥ w ρ (A) −m. The equality holds if and only if A is a multiple of a unitary operator.

Operator Radii of Commuting Products

Operator radii wp(T) for a bounded linear operator T on a Hubert space were introduced in connection with unitary p-dilations. We shall be concerned with universal estimates for the ratios wp(ST)/(wa(S)wl,(T)) for commuting operators S, T and o, p > 0. 1. All operators in this paper are bounded linear operators on a complex Hubert space §. We say an operator T belongs to the class G (0 < p < oo...

Operator Norm Convergence of Spectral Clustering on Level Sets

Following Hartigan [1975], a cluster is defined as a connected component of the t-level set of the underlying density, i.e., the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our algorithm is composed of two steps. First, a nonparametric density estimate is used to extract the data...

Interconnected Systems with Uncertain Couplings: Explicit Formulae for mu-Values, Spectral Value Sets, and Stability Radii

In this paper we study the variation of the spectrum of block-diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations (“Gershgorin-type perturbations”). We derive explicit and computable formulae for the associated μ-values. The results are then applied to characterize spectral value sets and stability radii for such perturbe...