Isometries between function algebras with finite codimensional range |
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Authors: | Juan J Font |
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Institution: | Departamento de Matemáticas, Universitat Jaume I, Campus Riu Sec,?E-12071 Castellón, Spain. E-mail: font@mat.uji.es, ES
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Abstract: | Let A be a function algebra on a compact space X. A linear isometry T of A into A is said to be codimension n or finite codimensional if the range of T has codimension n in A. In this paper we prove that such isometries can be represented as weighted composition mappings on a cofinite subset, (∂A)0, of the Shilov boundary for A, ∂A. We focus on those finite codimensional isometries for which (∂A)0=∂A. All the above results, applied to the particular case of codimension 1 linear isometries on C(X), are used to improve the classification provided by Gutek et al. in J. Funct. Anal. 101, 97–119 (1991).
Received: 3 June 1998 / Revised version: 22 March 1999 |
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Keywords: | Mathematics Subject Classification (1991):Primary 47B38 46J10 Secondary 46E25 |
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