We characterize a class of *-homomorphisms on Lip⁎(X,𝓑(𝓗 )), a non-commutative Banach *-algebra of Lipschitz functions on a compact metric space and with values in 𝓑(𝓗 ). We show that the zero map is the only multiplicative *-preserving linear functional on Lip⁎(X,𝓑(𝓗 )). We also establish the algebraic reflexivity property of a class of *-isomorphisms on Lip⁎(X,𝓑(𝓗 )).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-6,
author = {Fernanda Botelho and James Jamison},
title = {Homomorphisms on algebras of Lipschitz functions},
journal = {Studia Mathematica},
volume = {196},
year = {2010},
pages = {95-106},
zbl = {1216.47064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-6}
}
Fernanda Botelho; James Jamison. Homomorphisms on algebras of Lipschitz functions. Studia Mathematica, Tome 196 (2010) pp. 95-106. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm199-1-6/