A locally compact group has the Haagerup property, or is
a-T-menable in the sense of Gromov, if it admits a proper isometric
action on some affine Hilbert space. As Gromov's pun is trying to
indicate, this definition is designed as a strong negation to
Kazhdan's property (T), characterized by the fact that every
isometric action on some affine Hilbert space has a fixed
point.
The aim of this book is to cover, for the first time in book
form, various aspects of the Haagerup property. New
characterizations are brought in, using ergodic theory or operator
algebras. Several new examples are given, and new approaches to
previously known examples are proposed. Connected Lie groups with
the Haagerup property are completely characterized.
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