Strictly diagonal holomorphic functions on Banach spaces - Fedak, O.I.; Zagorodnyuk, A.V. (Carpathian Mathematical Publications, 2015)
In this paper we investigate the boundedness of holomorphic functionals on a Banach space with a normalized basis {e_n} which have a very special form f(x)=f(0)+_n=1^∞ c_nx_n^n and which we call strictly diagonal. We consider under which conditions strictly diagonal functions are entire and uniformly continuous on every ball of a fixed radius.