We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$.
By appealing to the injective tensor product, we then identify the character space of the vector-valued polynomial Lipschitz algebra $Lip_P^{alpha}(X, E)$, generated by the polynomials on the compact space $Xsubseteq Bbb{C}^{n}$. It is also shown that $Lip_P^{alpha}(X, E)$ is the injective tensor product $Lip_P^{alpha}(X)widehat{otimes}_epsilon E$. Finally, we characterize the form of each character on $Lip_{P}^{alpha}(X, E)$.
Honary, T., Nikou, A., & Sanatpour, A. H. (2014). On the character space of vector-valued Lipschitz algebras. Bulletin of the Iranian Mathematical Society, 40(6), 1453-1468.
MLA
T. Honary; A. Nikou; A. H. Sanatpour. "On the character space of vector-valued Lipschitz algebras". Bulletin of the Iranian Mathematical Society, 40, 6, 2014, 1453-1468.
HARVARD
Honary, T., Nikou, A., Sanatpour, A. H. (2014). 'On the character space of vector-valued Lipschitz algebras', Bulletin of the Iranian Mathematical Society, 40(6), pp. 1453-1468.
VANCOUVER
Honary, T., Nikou, A., Sanatpour, A. H. On the character space of vector-valued Lipschitz algebras. Bulletin of the Iranian Mathematical Society, 2014; 40(6): 1453-1468.
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