Lipschitz Algebras and Peripherally-multiplicative Maps  

作　　者：A.JIM■NEZ-VARGAS Moisés VILLEGAS-VALLECILLOS 

机构地区：[1]Departamento de■lgebray Análisis Matemático,Universidad de Almería,04071,Almería,Spain

出　　处：《Acta Mathematica Sinica,English Series》2008年第8期1233-1242,共10页数学学报（英文版）

基　　金：MEC project MTM2006-4837;Junta de Andalucia projects P06-FQM-1215 and P06-FQM-1438

摘　　要：Let X be a compact metric space and let Lip（X） be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip（X）, σπ（f） denotes the peripheral spectrum of f. We state that any map Φ from Lip（X） onto Lip（Y） which preserves multiplicatively the peripheral spectrum： σπ（Φ（f）Φ（g）） = σπ（fg）, A↓f, g ∈ Lip（X） is a weighted composition operator of the form Φ（f） = τ· （f °φ） for all f ∈ Lip（X）, where τ ： Y → {-1, 1} is a Lipschitz function and φ ： Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip（X）-algebras is of the form above.Let X be a compact metric space and let Lip（X） be the Banach algebra of all scalar- valued Lipschitz functions on X, endowed with a natural norm. For each f ∈ Lip（X）, σπ（f） denotes the peripheral spectrum of f. We state that any map Φ from Lip（X） onto Lip（Y） which preserves multiplicatively the peripheral spectrum： σπ（Φ（f）Φ（g）） = σπ（fg）, A↓f, g ∈ Lip（X） is a weighted composition operator of the form Φ（f） = τ· （f °φ） for all f ∈ Lip（X）, where τ ： Y → {-1, 1} is a Lipschitz function and φ ： Y→ X is a Lipschitz homeomorphism. As a consequence of this result, any multiplicatively spectrum-preserving surjective map between Lip（X）-algebras is of the form above.

关 键 词：Lipschitz algebra peripherally-multiplicative map spectrum-preserving map peaking function peripheral spectrum 

分 类 号：O152.5[理学—数学]