Positivity

, Volume 15, Issue 1, pp 161–174

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

Authors

  • Franciszek Hugon Szafraniec
    • Instytut MatematykiUniwersytet Jagielloński
    • Instytut MatematykiUniwersytet Jagielloński
Article

DOI: 10.1007/s11117-010-0048-x

Cite this article as:
Szafraniec, F.H. & Wojtylak, M. Positivity (2011) 15: 161. doi:10.1007/s11117-010-0048-x
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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.

Keywords

*-SemigroupShift operatorPontryagin spaceFundamental symmetry

Mathematics Subject Classification (2000)

Primary 43A3546C2047B32
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© Birkhäuser / Springer Basel AG 2010