Order isomorphisms of little Lipschitz algebras

• Autores: Antonio Jiménez Vargas , Moisés Villegas-Vallecillos
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 4, 2008, págs. 1185-1196
• Idioma: inglés
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• Resumen

  • For compact metric spaces (X,dX) and (Y,dY) and scalars a, ß in (0,1), we prove that every order isomorphism T between little Lipschitz algebras lip(X,(dX)a) and lip(Y,(dY)ß) is a weighted composition operator of the form Tf(y) = a(y)f(h(y)) for all f in lip(X,(dX)a) and all y in Y, where a is a nonvanishing positive function in lip(Y,(dY)ß) and h is a Lipschitz homeomorphism from (Y,(dY)ß) onto (X,(dX)a)