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Isometries between function algebras with finite codimensional range
- Source :
- manuscripta mathematica. 100:13-21
- Publication Year :
- 1999
- Publisher :
- Springer Science and Business Media LLC, 1999.
-
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).
Details
- ISSN :
- 14321785 and 00252611
- Volume :
- 100
- Database :
- OpenAIRE
- Journal :
- manuscripta mathematica
- Accession number :
- edsair.doi...........0980d59771210aadbba175f0a2e66ae8
- Full Text :
- https://doi.org/10.1007/s002290050192