A minimal property for an operator of Hilbert-Schmidt class

The Hilbert-Schmidt property of feedback operators

Ruth Curtain Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. E-mail:[email protected], Kalle Mikkola Helsinki University of Technology, Institute of Mathematics, Box 1100, 02015 HUT, Finland. E-mail:[email protected], Amol Sasane Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom....

Radonification of Cylindrical Semimartingales by a Single Hilbert Schmidt Operator

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.

Trace class operators and Hilbert-Schmidt operators

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

OPERATOR THEORY ON HILBERT SPACE Class notes

Hilbert–Schmidt component analysis

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.