## Banach Journal of Mathematical Analysis

### Linear isometries of finite codimensions on Banach algebras of holomorphic functions

#### Abstract

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 information

Source
Banach J. Math. Anal., Volume 3, Number 2 (2009), 109-124.

Dates
First available in Project Euclid: 17 December 2009

https://projecteuclid.org/euclid.bjma/1261086715

Digital Object Identifier
doi:10.15352/bjma/1261086715

Mathematical Reviews number (MathSciNet)
MR2661119

Zentralblatt MATH identifier
1193.46006

#### Citation

Hatori, Osamu; Kasuga, Kazuhiro. Linear isometries of finite codimensions on Banach algebras of holomorphic functions. Banach J. Math. Anal. 3 (2009), no. 2, 109--124. doi:10.15352/bjma/1261086715. https://projecteuclid.org/euclid.bjma/1261086715