Geodesic
Homomorphisms on algebras of Lipschitz functions
Fernanda Botelho1 ; James Jamison1
1Department of Mathematical Sciences The University of Memphis Memphis, TN 38152, U.S.A.
Studia Mathematica, Tome 199 (2010) no. 1, pp. 95-106
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We characterize a class of $*$-homomorphisms on ${\rm Lip}_*(X, \mathcal{B}(\mathcal{H})),$ a non-commutative Banach $*$-algebra of Lipschitz functions on a compact metric space and with values in $\mathcal{B}(\mathcal{H}).$ We show that the zero map is the only multiplicative $\ast $-preserving linear functional on ${\rm Lip}_*(X, \mathcal{B}(\mathcal{H})).$ We also establish the algebraic reflexivity property of a class of $*$-isomorphisms on ${\rm Lip}_*(X, \mathcal{B}(\mathcal{H})).$
DOI : 10.4064/sm199-1-6
Mots-clés : characterize class * homomorphisms lip * mathcal mathcal non commutative banach * algebra lipschitz functions compact metric space values mathcal mathcal zero map only multiplicative ast preserving linear functional lip * mathcal mathcal establish algebraic reflexivity property class * isomorphisms lip * mathcal mathcal

Fernanda Botelho  1   ; James Jamison  1

1 Department of Mathematical Sciences The University of Memphis Memphis, TN 38152, U.S.A. 
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Fernanda Botelho; James Jamison. Homomorphisms on algebras of Lipschitz functions. Studia Mathematica, Tome 199 (2010) no. 1, pp. 95-106. doi: 10.4064/sm199-1-6

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