Projectively invariant Hilbert-Schmidt kernels and convolution type operators

• Autorzy: Jaeseong Heo
• Języki publikacji: EN

Abstrakty

EN

We consider positive definite kernels which are invariant under a multiplier and an action of a semigroup with involution, and construct the associated projective isometric representation on a Hilbert C*-module. We introduce the notion of C*-valued Hilbert-Schmidt kernels associated with two sequences and construct the corresponding reproducing Hilbert C*-module. We also discuss projective invariance of Hilbert-Schmidt kernels. We prove that the range of a convolution type operator associated with a Hilbert-Schmidt kernel coincides with the reproducing Hilbert C*-module associated with its convolution kernel. We show that the integral operator associated with a Hilbert-Schmidt kernel is Hilbert-Schmidt. Finally, we discuss a relation between an integral type operator and convolution type operator.

Kategorie tematyczne

• 46N55: Applications in statistical physics
• 46L08: C * -modules
• 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
• 46C50: Generalizations of inner products (semi-inner products, partial inner products, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 213
• Numer: 1
• Strony: 61-79

Daty

wydano

2012

Twórcy

autor

Jaeseong Heo

• Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea

Identyfikatory

DOI

10.4064/sm213-1-5