Pontryagin Space Structure in Reproducing Kernel Hilbert Spaces over *-semigroups
Functional Analysis
2009-07-08 v1
Abstract
The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries
Cite
@article{arxiv.0907.1172,
title = {Pontryagin Space Structure in Reproducing Kernel Hilbert Spaces over *-semigroups},
author = {Franciszek Hugon Szafraniec and Michal Wojtylak},
journal= {arXiv preprint arXiv:0907.1172},
year = {2009}
}