an: Zbl 1193.46006
au: Hatori, Osamu; Kasuga, Kazuhiro
ti: Linear isometries of finite codimensions on Banach algebras of holomorphic
    functions.
la: EN
so: Banach J. Math. Anal. 3, No. 2, 109-124, electronic only (2009).
py: 2009
dt: J
cc: *46B04 32A38 46J15
ut: shift operators; isometries; uniform algebra
ab: 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.