International Journal of Mathematics and Mathematical Sciences 
Volume 32 (2002), Issue 3, Pages 189-192
doi:10.1155/S0161171202203348

A note on a class of Banach algebra-valued polynomials

Sin-Ei Takahasi,1 Osamu Hatori,2 Keiichi Watanabe,3 and Takeshi Miura1

 1Department of Basic Technology, Applied Mathematics and Physics, Yamagata University, Yonezawa 992-8510, Japan
2Department of Mathematical Sciences, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
3Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
Received 10 March 2002

Abstract

Let F be a Banach algebra. We give a necessary and sufficient condition for F to be finite dimensional, in terms of finite type n-homogeneous F-valued polynomials.