# Real-linear isometries between function algebras

Open Mathematics (2011)

- Volume: 9, Issue: 4, page 778-788
- ISSN: 2391-5455

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topTakeshi Miura. "Real-linear isometries between function algebras." Open Mathematics 9.4 (2011): 778-788. <http://eudml.org/doc/269446>.

@article{TakeshiMiura2011,

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

author = {Takeshi Miura},

journal = {Open Mathematics},

keywords = {Commutative Banach algebra; Function algebra; Isometry; Isomorphism; Uniform algebra; function algebra; Choquet boundary; surjection; isometry; isomorphism; homeomorphism},

language = {eng},

number = {4},

pages = {778-788},

title = {Real-linear isometries between function algebras},

url = {http://eudml.org/doc/269446},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Takeshi Miura

TI - Real-linear isometries between function algebras

JO - Open Mathematics

PY - 2011

VL - 9

IS - 4

SP - 778

EP - 788

AB - 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.

LA - eng

KW - Commutative Banach algebra; Function algebra; Isometry; Isomorphism; Uniform algebra; function algebra; Choquet boundary; surjection; isometry; isomorphism; homeomorphism

UR - http://eudml.org/doc/269446

ER -

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