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Title: On dilation of local semigroups of contractions and some applications
Authors: Bruzual, Ramón
Domínguez, Marisela
Padilla, Ángel
Universidad Central de Venezuela
Keywords: Operator semigroup
Contraction operator
Isometric operator
Positive definite
Semigrupo del operador
Operador de contracción
Operador isométrico
Positivo definido
Issue Date: 2012
Publisher: Universidad de Extremadura
Abstract: We show that a multiplicative family of contractions on a separable Hilbert space, with parameter on the interval [0, 1) of the dyadic rationals, has a unitary dilation with parameter on the dyadic rationals and values on a larger Hilbert space. This result is used to prove a dilation result for strongly continuous local semigroups of contractions. As an application we give results of extension of positive definite functions on the line, generalizing the Kreĭn extension theorem.
Appears in Collections:Extracta Mathematicae Vol. 27, nº 2 (2012)

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