Let $K$ be a compact subset of the complex $n$-space and $A(K)$ the algebra of
all continuous functions on $K$ which are holomorphic on the interior of $K$. In
this paper we show that under some hypotheses on $K$, there exists no linear
isometry of finite codimension on $A(K)$. Several compact subsets including the
closure of strictly pseudoconvex domain and the product of the closure of plane
domains which are bounded by a finite number of disjoint smooth curves satisfy
the hypotheses.
@article{1261086715,
author = {Hatori, Osamu and Kasuga, Kazuhiro},
title = {Linear isometries of finite codimensions on Banach algebras of holomorphic
functions},
journal = {Banach J. Math. Anal.},
volume = {3},
number = {2},
year = {2009},
pages = { 109-124},
language = {en},
url = {http://dml.mathdoc.fr/item/1261086715}
}
Hatori, Osamu; Kasuga, Kazuhiro. Linear isometries of finite codimensions on Banach algebras of holomorphic
functions. Banach J. Math. Anal., Tome 3 (2009) no. 2, pp. 109-124. http://gdmltest.u-ga.fr/item/1261086715/