Compact Hankel operators and the F. and M. Riesz theorem

Lavon Barry Page

Vol. 56 (1975), No. 1, 221–223

DOI: 10.2140/pjm.1975.56.221

Abstract

The F. and M. Riesz theorem asserts that every complex Borel measure on the unit circle whose Fourier coefficients with negative index vanish is necessarily absolutely continuous with respect to Lebesgue measure.

The purpose of this note is to give a new proof of Hartman’s theorem on compact Hankel operators which clarifies the general context of the theorem. The proof depends only on a few simple operator-theoretic results, Nehari’s characterization of bounded Hankel operators, and the aforementioned theorem of F. and M. Riesz.

Mathematical Subject Classification 2000

Primary: 47B35

Milestones

Received: 25 September 1973

Published: 1 January 1975