Strictly diagonal holomorphic functions on Banach spaces

O. I. Fedak, A. V. Zagorodnyuk

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.


Keywords


holomorphic functions on Banach spaces, bases on Banach spaces

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