Real-linear isometries between function algebras |
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Authors: | Takeshi Miura |
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Affiliation: | 1.Department of Basic Technology, Applied Mathematics and Physics,Yamagata University,Yonezawa,Japan |
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Abstract: | Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → {z ∈ ℂ: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and T( f ) = k[`(fof)]Tleft( f right) = kappa overline {fophi } on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras. |
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