Kazhdan's Property (T)
In mathematics, a locally compact topological group G has property (T) if the trivial representation is an isolated point in its unitary dual equipped with the Fell topology. Informally, this means that if G acts unitarily on a Hilbert space and has "almost invariant vectors", then it has a nonzero invariant vector. The formal definition, introduced by David Kazhdan (1967), gives this a precise, quantitative meaning.
Although originally defined in terms of irreducible representations, property (T) can often be checked even when there is little or no explicit knowledge of the unitary dual. Property (T) has important applications to group representation theory, lattices in algebraic groups over local fields, ergodic theory, geometric group theory, expanders, operator algebras and the theory of networks.
Read more about Kazhdan's Property (T): Definitions, Discussion, General Properties, Examples, Discrete Groups, Applications
Famous quotes containing the word property:
“Never let the estate decrease in your hands. It is only by such resolutions as that that English noblemen and English gentlemen can preserve their country. I cannot bear to see property changing hands.”
—Anthony Trollope (1815–1882)