##### Department of Mathematics,

University of California San Diego

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### Math 243 - Functional Analysis

## Benjamin Hayes

#### University of Virginia

## Quotients of Bernoulli shifts associated to operators with an $\ell^{2}$-inverse.

##### Abstract:

Let G be a countable, discrete, group and f an element of the integral group ring over G. It is well known how to associate to f an action of G on a compact, metrizable, abelian group. It turns out to be particularly interested to consider those f with an $\ell^{2}$-inveres: i.e. a vector $\xi\in \ell^{2}(G)$ so that $f*\xi=\delta_{1}$. Many nice ergodic theoretic properties of the corresponding action have been established in this context. I will give certain examples of f,G for which we can say that this action is a quotient of a Bernoulli shift. When G is amenable, this implies that it *is* a Bernoulli shift.

Host: Todd Kemp

### February 8, 2019

### 10:00 AM

### AP&M 6402

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