Spectra for Toeplitz Operators Associated with a Constrained Subalgebra

Abstract

A two-point algebra is a set of bounded analytic functions on the unit disk that agree at two distinct points 𝑎,𝑏∈𝔻. This algebra serves as a multiplier algebra for the family of Hardy Hilbert spaces 𝐻2𝑡:={𝑓∈𝐻2:𝑓(𝑎)=𝑡𝑓(𝑏)}, where 𝑡∈ℂ∪{∞}. We show that various spectra of certain Toeplitz operators acting on these spaces are connected.