@article{1193.46006,
author="Hatori, Osamu and Kasuga, Kazuhiro",
title="{Linear isometries of finite codimensions on Banach algebras of
    holomorphic functions.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="3",
number="2",
pages="109-124",
year="2009",
abstract="{Summary: 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.}",
keywords="{shift operators; isometries; uniform algebra}",
classmath="{*46B04 (Isometric theory of Banach spaces)
32A38 (Algebras of holomorphic functions of several variables)
46J15 (Banach algebras of differentiable functions)
}",
}