Strictly diagonal holomorphic functions on Banach spaces
Keywords:
holomorphic functions on Banach spaces, bases on Banach spaces
Published online:
2015-12-24
Abstract
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.
How to Cite
(1)
Fedak, O.; Zagorodnyuk, A. Strictly Diagonal Holomorphic Functions on Banach Spaces. Carpathian Math. Publ. 2015, 7, 254-258.