Strictly diagonal holomorphic functions on Banach spaces


  • O.I. Fedak Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 79060, Lviv, Ukraine
  • A.V. Zagorodnyuk Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine


holomorphic functions on Banach spaces, bases on Banach spaces
Published online: 2015-12-24


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.

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How to Cite
Fedak, O.; Zagorodnyuk, A. Strictly Diagonal Holomorphic Functions on Banach Spaces. Carpathian Math. Publ. 2015, 7, 254-258.