# On the character space of vector-valued Lipschitz algebras

Document Type : Research Paper

Authors

Kharazmi University

Abstract

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 $Lip_{P}^{alpha}(X, E)$.

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Main Subjects

### History

• Receive Date: 04 March 2013
• Revise Date: 19 October 2013
• Accept Date: 20 October 2013