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A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let C c ( G ) be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that ( C c ( G ) , ε G ) has property (FH) if and only if G has property (T). On...

A ratio ergodic theorem for multiparameter non-singular actions

Michael Hochman (2010)

Journal of the European Mathematical Society

We prove a ratio ergodic theorem for non-singular free d and d actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in d . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group...

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