The Schatten quasi-norm was introduced tobridge the gap between the trace norm andrank function. However, existing algorithmsare too slow or even impractical for large-scale problems. Motivated by the equivalencerelation between the trace norm and its bilin-ear spectral penalty, we define two tractableSchatten norms, i.e. the bi-trace and tri-tracenorms, and prov...

Let A belong to the Schatten-von Neumann ideal Sp for 0 < p < ∞. We give an upper bound for the operator norm of the resolvent (zI − A)−1 of A in terms of the departure from normality of A and the distance of z to the spectrum of A. As an application we provide an upper bound for the Hausdorff distance of the spectra of two operators belonging to Sp.

We study the first and second orders of asymptotic expansion, as dimension goes to infinity, moments Hilbert-Schmidt norm a uniformly distributed matrix in p-Schatten unit ball. consider case matrices with real, complex or quaternionic entries, self-adjoint not. When p>3, this expansion allows us establish generalized version variance conjecture for family balls matrices.

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues, we propose a scalable core tensor trace norm Regularized Orthogonal Iteration Decomposition (ROID) method for full or incomplete tensor analytics, which can...

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I⊗Φ) ( |ψ〉〈ψ| ) . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatt...

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l₁-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptim...

Let A be a C *-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (A t) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. Then the following equality including Bouchner integrals holds T A t − T A s dP 2 dP = T |A t | 2 dP − T A t dP 2. (0.1) This equality is relat...

The related inequality (1.1) was obtained by Maher [3, Theorem 3.2] who showed that, if A is normal and AT = TA, where T ∈ Cp , then ‖T − (AX −XA)‖p ≥ ‖T‖p for all X ∈ ( ), where Cp is the von Neumann-Schatten class, 1≤ p <∞, and ‖·‖p its norm. Here we show that Maher’s result is also true in the case where Cp is replaced by ( ), the ideal of all compact operators with ‖·‖∞ its norm.Which allow...

MICHAEL K. TIPPETTy, STEPHEN E. COHNz, RICARDO TODLINGx, AND DAN MARCHESIN{ Abstract. The Schatten p-norm condition of the discrete-time Lyapunov operator LA defined on matrices P 2 Rn n by LAP P APAT is studied for stable matrices A 2 Rn n . Bounds are obtained for the norm of LA and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of ...

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represent by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I ⊗Φ) ( |ψ〉〈ψ| ) We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatten ...