International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 3, Pages 189-192

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

Copyright © 2002 Sin-Ei Takahasi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.