ASYMPTOTIC INTERPOLATING SEQUENCES IN UNIFORM ALGEBRAS

Abstract

T. Hosokawa, K. Izuchi and D. Zheng recently introduced the concept of asymptotic interpolating sequences (of type 1) in the unit disk for $H^\infty$(${\bb D}$). It is shown that these sequences coincide with sequences that are interpolating for the algebra $QA$. Also a characterization is given of the interpolating sequences of type $1$ for $H^\infty$(${\bb D}$), and asymptotic interpolating sequences in the spectrum of $H^\infty$(${\bb D}$) are studied. The existence of asymptotic interpolating sequences of type $1$ for $H^\infty(\Omega)$ on arbitrary domains is verified. It is shown that any asymptotic interpolating sequence in a uniform algebra eventually is interpolating.