## Some thoughts about Segal's ergodic theorem

### Volume 118 / 2010

Colloquium Mathematicum 118 (2010), 89-105
MSC: 60G15, 60G17.
DOI: 10.4064/cm118-1-4

#### Abstract

Over fifty years ago, Irving Segal proved a theorem which leads to a characterization of those orthogonal transformations on a Hilbert space which induce ergodic transformations. Because Segal did not present his result in a way which made it readily accessible to specialists in ergodic theory, it was difficult for them to appreciate what he had done. The purpose of this note is to state and prove Segal's result in a way which, I hope, will win it the recognition which it deserves.