Abstract

1. Positive definite forms. Suppose S is an involution semigroup and E is a complex linear space. Let o9: S • 2 1 5 be a map such that for every sES ~o(s , . , ) is a (hermitian) bilinear form. We call ~o simply a form (over (S, E)) although it is in fact a family of forms on E, indexed by S. We will see a little while later that we are not far f rom being precise at this point. We say that a form 09 is positive definite (in short: PD) if for all finite sequences sl . . . . . s,E S and f l . . . . . f , EE

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