Norms of linear functionals on the space of bounded analytic functions on an annulus

Abstract

Many functionals on the space of bounded analytic functions on an annulus are defined in terms of a multiplier sequence for the Laurent series. This paper studies the norms of such functionals in terms of a real valued function which induces the functional by integration along the boundary. An application is that symmetric partial sums of the Laurent series give functionals of norm 1 on proper subannuli. Another is a characterization of the Hilbert space operators having the annulus as a spectral set.

AMS (MOS):

• 46J15
• 30B10
• 47A25