Projectively invariant Hilbert-Schmidt kernels and convolution type operators

Jaeseong Heo. "Projectively invariant Hilbert-Schmidt kernels and convolution type operators." Studia Mathematica 213.1 (2012): 61-79. <http://eudml.org/doc/285798>.

@article{JaeseongHeo2012,
abstract = {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.},
author = {Jaeseong Heo},
journal = {Studia Mathematica},
keywords = {-valued positive definite kernel; -valued Hilbert-Schmidt kernel; convolution type operator; convolution kernel; reproducing kernel Hilbert -module},
language = {eng},
number = {1},
pages = {61-79},
title = {Projectively invariant Hilbert-Schmidt kernels and convolution type operators},
url = {http://eudml.org/doc/285798},
volume = {213},
year = {2012},
}

TY - JOUR
AU - Jaeseong Heo
TI - Projectively invariant Hilbert-Schmidt kernels and convolution type operators
JO - Studia Mathematica
PY - 2012
VL - 213
IS - 1
SP - 61
EP - 79
AB - 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.
LA - eng
KW - -valued positive definite kernel; -valued Hilbert-Schmidt kernel; convolution type operator; convolution kernel; reproducing kernel Hilbert -module
UR - http://eudml.org/doc/285798
ER -