In this note it is shown that the Hilbert-Schmidt-Hankel norm (HSH-norm) of a transfer function of a stable system is equal, up to a constant factor, to the square root of the area enclosed by the oriented Nyquist diagram of the transfer function (multiplicities included). A generalization is presented for the case of systems which have no poles on the stability boundary, but otherwise have no ...

Quantum discord is a manifestation of quantum correlations due to non-commutativity rather than entanglement. Two measures of quantum discord by the amount of non-commutativity via the trace norm and the Hilbert-Schmidt norm respectively are proposed in this paper. These two measures can be calculated easily for any state with arbitrary dimension. It is shown by several examples that these meas...

Composition operators Cφ on the Hilbert Hardy space H 2 over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn → Cφ . If the composition operators Cφn are Hilbert–Schmidt operators, we prove that convergence in the Hi...

We investigate composition-differentiation operators acting on the Dirichlet space of unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt operators. In addition, particular classes inducing maps, derive an adjoint formula, compute norm, identify spectrum.

We propose an independence criterion based on the eigenspectrum of covariance operators in reproducing kernel Hilbert spaces (RKHSs), consisting of an empirical estimate of the Hilbert-Schmidt norm of the cross-covariance operator (we term this a Hilbert-Schmidt Independence Criterion, or HSIC). This approach has several advantages, compared with previous kernel-based independence criteria. Fir...

* Correspondence: limin-zou@163. com School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, People’s Republic of China Abstract We obtain an improved Heinz inequality for scalars and we use it to establish an inequality for the Hilbert-Schmidt norm of matrices, which is a refinement of a result due to Kittaneh. Mathematical Subject Classification 2010: 26D07;...

The space of upper triangular matrices with Hilbert{Schmidt norm can be viewed as a nite dimensional analogue of the Hardy space H2 of the unit disk when one introduces the adequate notion of \point" evaluation. A bitangential interpolation problem in this setting is studied. The description of all solution in terms of Beurling{Lax representation is given.

This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator trace-class operator-valued integrated volatility process arising in general mild solutions Hilbert space-valued evolution equations sense Da Prato and Zabczyk (2014). We prove a weak law large numbers for t...

A Banach space X has the 2-summing property if the norm of every linear operator from X to a Hilbert space is equal to the 2-summing norm of the operator. Up to a point, the theory of spaces which have this property is independent of the scalar eld: the property is self-dual and any space with the property is a nite dimensional space of maximal distance to the Hilbert space of the same dimensio...