Operator algebras related to measure preserving transformations of finite order (Q1063849)

The author investigates operators of the form \[ Tf=\sum^{N- 1}_{i=0}a_ if\circ \tau^ i, \] where \(\tau\) is a periodic (with period N) measure-preserving transformation of a finite measure space, and each \(a_ i\) is a measurable function. It is shown that if T defines a bounded operator on \(L_ 2\) then \(a_ i\in L_{\infty}\), and that the set of all such operators is a von Neumann algebra. Moreover, the spectrum of T is described.