An examle of the Normality

Abstract

Throughout this paper, all algebras are considered over the complex field C. We discuss the normality of a normed space D(K,M), where K is a perfect, compact subset of C and M (MA)nzo is a sequence of positive numbers. It is standard that, if int(K) (the interior of K) is nonempty and M is any sequence, then D(K,M) is not normal on K. We give an example where D(K, M) is normal on K. This means that we need to find K.with an empty int(K) and a non-quasi-analytic sequence M.