RT Journal Article
T1 Derivative and factorization of holomorphic functions
A1 Bombal Gordon, Fernando
A1 Gutiérrez, Joaquín M.
A1 Villanueva Díez, Ignacio
AB Let E  be a complex Banach space and denote by H b (E)  the space of all holomorphic functions f:E→C  of bounded type, that is, bounded on bounded sets. It is known that f∈H b (E)  admits a factorization of the form f=g∘S  , with S  a compact linear operator and g  a holomorphic function of bounded type if and only if the derivative df:E→E ∗   takes bounded sets of E  into relatively compact sets of E ∗   . In the weakly compact case, a similar result was obtained by R. M. Aron and P. Galindo [Proc. Edinburgh Math. Soc. (2) 40 (1997), no. 1, 181–192;]. In the paper under review, the authors extend these results to closed injective operator ideals and the associated families of bounded sets. Moreover, this main result is applied to give examples of factorization through operators belonging to important closed injective operator ideals.
PB Elsevier
SN 0022-247X
YR 2008
FD 2008-12-01
LK https://hdl.handle.net/20.500.14352/50479
UL https://hdl.handle.net/20.500.14352/50479
LA eng
NO Dirección General de Investigación
NO Universidad Complutense de Madrid
DS Docta Complutense
RD 8 abr 2025