TY - JOUR ID - 576 TI - On the character space of vector-valued Lipschitz algebras JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Honary, T. AU - Nikou, A. AU - Sanatpour, A. H. AD - Kharazmi University Y1 - 2014 PY - 2014 VL - 40 IS - 6 SP - 1453 EP - 1468 KW - Vector-valued Lipschitz algebras KW - character space KW - injective tensor product KW - polynomial approximation DO - N2 - 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 $Lip_{P}^{alpha}(X, E)$. UR - http://bims.iranjournals.ir/article_576.html L1 - http://bims.iranjournals.ir/article_576_f9f5524bf4345a77d76c6c1453d51115.pdf ER -