Oleg N. Ageev
Spectral Rigidity of Group Actions: Applications to the Case gr $\langle t,s ; ts=st^2\rangle$
The paper is published: Proc. Amer. Math. Soc. 134 (2006) 1331-1338

MSC:

28D05 Measure-preserving transformations

28D15 General groups of measure-preserving transformations

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)

47A35 Ergodic theory, See also {28Dxx}

47D03 (Semi)groups of linear operators, {For nonlinear operators, See 47H20; See also 20M20}

Abstract: We apply a technique to study the notion of spectral rigidity
of group actions to a group $\mbox{gr}\langle t,s ; \ ts=st^2\rangle$.
As an application, we prove that there exist rank one weakly mixing
transformations conjugate its square, thereby giving a positive answer to a well-known question.

Keywords: group actions, ergodic theory, conjugations to its squares