Open AccessStrictly diagonal holomorphic functions on Banach spaces
Author(s) -
O.I. Fedak,
Andriy Zagorodnyuk
Publication year - 2015
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.7.2.254-258
Subject(s) - mathematics , holomorphic function , diagonal , banach space , pure mathematics , ball (mathematics) , mathematical analysis , discrete mathematics , combinatorics , geometry
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 $f(x)=f(0)+\sum_{n=1}^\infty c_nx_n^n$ 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.