On the spectral multiplicity of a class of finite rank transformations
Geoffrey R. Goodson · Proceedings of the American Mathematical Society · 1985
The rank M M transformations, which Chacon called the simple approximations with multiplicity M M , were shown by Chacon to have maximal spectral multiplicity at most M M , although no example was given where this bound is attained for M > 1 M > 1 . In this paper, for each natural number M > 1 M > 1 , we show how to construct a simple approximation with multiplicity M M which is ergodic and has maximal spectral multiplicity equal to M − 1 M - 1 .