Projectively invariant Hilbert-Schmidt kernels and convolution type operators
- Authors
- Heo, Jaeseong
- Issue Date
- Dec-2012
- Publisher
- POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN
- Keywords
- C*-valued positive definite kernel; C*-valued Hilbert-Schmidt kernel; convolution type operator; convolution kernel; reproducing kernel Hilbert C*-module
- Citation
- STUDIA MATHEMATICA, v.213, no.1, pp.61 - 79
- Indexed
- SCIE
SCOPUS
- Journal Title
- STUDIA MATHEMATICA
- Volume
- 213
- Number
- 1
- Start Page
- 61
- End Page
- 79
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/164028
- DOI
- 10.4064/sm213-1-5
- ISSN
- 0039-3223
- 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.
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