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.

We propose a feature extraction algorithm, based on the Hilbert–Schmidt independence criterion (HSIC) and the maximum dependence – minimum redundancy approach. Experiments with classification data sets demonstrate that suggested Hilbert–Schmidt component analysis (HSCA) algorithm in certain cases may be more efficient than other considered approaches.

It is proved that in Hilbert spaces a single Hilbert–Schmidt operator radonifies cylindrical semimartingales to strong semimartingales. This improves a result due to Badrikian and¨Ustünel (also L. Schwartz), who needed composition of three Hilbert–Schmidt operators.

This work studies the convergence and finite sample approximations of entropic regularized Wasserstein distances in Hilbert space setting. Our first main result is that for Gaussian measures on an infinite-dimensional space, 2-Sinkhorn divergence strictly weaker than exact 2-Wasserstein distance. Specifically, a sequence centered converges if corresponding covariance operators converge Hilbert–...

Entanglement calculations have received renewed interest with the advances observed in field of quantum computing. Alternative methods to calculate entanglement that can be applied broader classes problems become increasingly necessary. In this letter, we show measure using generalized Bell inequality and distance between states coincide when use Hilbert–Schmidt norm. Our conclusions apply spin...

Suppose that $${\mathscr {E}}$$ and {F}}$$ are Hilbert $$C^*$$ -modules. We present a power-norm $$\left( \left\| \cdot \right\| ^{{\mathscr {E}}}_n:n\in {\mathbb {N}}\right) $$ based on obtain some of its fundamental properties. introduce new definition the absolutely (2, 2)-summing operators from to , denote set such by $${\tilde{\Pi }}_2({\mathscr {E}},{\mathscr {F}})$$ with convention {E}})...