Toeplitz operators on H_p

Harold Widom

Vol. 19 (1966), No. 3, 573–582

DOI: 10.2140/pjm.1966.19.573

Abstract

A Toeplitz operator is an operator with a matrix representation (α_m−n)_m,n=0^∞ where the α_n are the Fourier coefficients of a bounded function φ. The operator may be considered as acting on any of the Hardy spaces H_p(1 < p < ∞) and it is the purpose of this note to show that the spectrum of any such operator is a connected set.

Mathematical Subject Classification

Primary: 47.25

Milestones

Received: 21 May 1965

Published: 1 December 1966