Given an action α of a discrete group G on a unital C∗-algebra A, we introduce a natural concept of α-negative definiteness for functions from G to A, and examine some of the first consequences of such a notion. In particular, we prove analogs of theorems due to Delorme–Guichardet and Schoenberg in the classical case where A is trivial. We also give a characterization of the Haagerup property for the action α when G is countable.
Negative definite functions for Câ-dynamical systems / Bédos, Erik; Conti, Roberto. - In: POSITIVITY. - ISSN 1385-1292. - STAMPA. - 21:4(2017), pp. 1625-1646. [10.1007/s11117-017-0490-0]
Negative definite functions for Câ-dynamical systems
Conti, Roberto
2017
Abstract
Given an action α of a discrete group G on a unital C∗-algebra A, we introduce a natural concept of α-negative definiteness for functions from G to A, and examine some of the first consequences of such a notion. In particular, we prove analogs of theorems due to Delorme–Guichardet and Schoenberg in the classical case where A is trivial. We also give a characterization of the Haagerup property for the action α when G is countable.File allegati a questo prodotto
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