Title of article :
On the character space of vector-valued Lipschitz algebras
Author/Authors :
Ghasemi Honary، Taher نويسنده Kharazmi University , , Nikou، Azadeh نويسنده Kharazmi University , , Sanatpour، Amir Hossein نويسنده Kharazmi University ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2014
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 $X\times M_E$
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 $X\subseteq \Bbb{C}^{n}$. 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 $Lip_{P}^{\alpha}(X, E)$.
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
