Real-linear isometries between function algebras

Takeshi Miura

Open Mathematics, Tome 9 (2011), p. 778-788 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $T\left( f \right) = \kappa \overline{fo\phi }$ on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.

Détail

Publié le : 2011-01-01

Zbl 1243.46043

EUDML-ID : urn:eudml:doc:269446

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