an:00753842
Zbl 0833.28008
Choksi, J. R.; Nadkarni, M. G.
The group of eigenvalues of a rank one transformation
EN
Can. Math. Bull. 38, No. 1, 42-54 (1995).
00025927
1995
j
28D05 47A35
\(L^ \infty\)-eigenvalues; maximal spectral type; rank one transformation
In an earlier paper [Can. Math. Bull. 37, No. 1, 29-36 (1994; Zbl 0793.28013)], the authors gave a description of the maximal spectral type of a rank one transformation \(T\), as a certain generalized Riesz product. Apparently it was suggested by J.-F. Mela that this description is related to the group \(e(T)\) of \(L^\infty\)-eigenvalues of \(T\). These are the \(L^2\)-eigenvalues when the underlying space is of finite measure, but the usual cutting and stacking construction for rank one maps allows the resulting measure space to be \(\sigma\)-finite.
Several characterizations of \(e(T)\) are given for rank one \(T\), one of which is intimately related to the corresponding expression for the maximal spectral type of \(T\).
G.R.Goodson (Towson)
Zbl 0793.28013