Pontryagin Space Structure in Reproducing Kernel Hilbert Spaces over *-semigroups

Franciszek Hugon Szafraniec, Michal Wojtylak

Published 2009-07-07Version 1

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