an:05702392 Zbl 1193.46006 Hatori, Osamu; Kasuga, Kazuhiro Linear isometries of finite codimensions on Banach algebras of holomorphic functions. EN Banach J. Math. Anal. 3, No. 2, 109-124, electronic only (2009). ISSN 1735-8787/e 2009

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*46B04 32A38 46J15 shift operators; isometries; uniform algebra 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.