On positive definite functions and representations of Clifford ω-semigroups
AbstractIt is known that a complex valued function f on a Clifford ω-semigroup, T=UnGn is positive definite if and only if its restriction fn to Gn, is positive definite for any positive integer n. Then, by the usual Gelfand-Naimark-Segal construction, f and fn (n\in ℕ ) give rise to the representations πf of T, respectively πfn of Gn. In this note we study the relationship between the restriction of πf to Gn and the representation of πfn(n\in ℕ ).
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