Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups
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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*-Semigroup Shift operator Pontryagin space Fundamental symmetry
Mathematics Subject Classification (2000)Primary 43A35 46C20 47B32
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