ON ISOMETRIES WITH FINITE SPECTRUM

Abstract

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.

Publication Title

Journal of Operator Theory

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