On the analytic structure of the $H^\infty$ maximal ideal space

Publication date: 29 October 2003

Abstract: We characterize the algebra

H^{i} n f t y c i r c L_{m}

, where

m

is a point of the maximal ideal space of

H^{i} n f t y

with nontrivial Gleason part

P (m)

and

L_{m} : m a t h b b D o P (m)

is the coordinate Hoffman map. In particular, it is shown that for any continuous function

f : P (m) o m a t h b b C

with

f c i r c L_{m} i n H^{i} n f t y

there exists

F i n H^{i} n f t y

such that

F |_{P (m)} = f

.