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Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

by Christopher Felder, Douglas Pfeffer, Benjamin P Russo
Publication Type
Journal
Journal Name
Integral Equations and Operator Theory
Publication Date
Page Numbers
1 to 19
Volume
94
Issue
2

A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points ๐‘Ž,๐‘โˆˆ๐”ป. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces ๐ป2๐‘ก:={๐‘“โˆˆ๐ป2:๐‘“(๐‘Ž)=๐‘ก๐‘“(๐‘)}, where ๐‘กโˆˆโ„‚โˆช{โˆž}. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.