ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47 Flytzanis, Elias, Athens University of Economics and Business, Greece An invariance property of Quadratic forms In complex Hilbert spaces we consider positive quadratic forms defined by self-adjoint positive operators S of finite trace. We show that the linear operators A that leave invariant such quadratic forms in the sense that < Ax, SAx >=< x, Sx >, are the operators for which the adjoint A^{∗} has a spanning set of eigenvectors of norm 1. We obtain this result by solving for A operator equations of the form KA = KU where U is an isometry and K is Hilbert-Smith. Reference: E. Flytzanis, Unimodular eigenvalues and Invariant measures for linear Operators. Monatshefte für Math. 119 (1995), 267–273.