ON ISOMETRIES WITH FINITE SPECTRUM

In this paper we investigate inverse eigenvalue problems for finite spectrum linear isometries on complex Banach spaces. We establish necessary conditions on a finite set of modulus one complex numbers to be the spectrum of a linear isometry. In particular, we study periodic linear isometries on the large class of Banach spaces X with the following property: if T: X X is a linear isometry with two-point spectrum {1, λ} then λ = —1 or the eigenprojections of T are Hermitian