The power series ^∞_n=0n!z^n and holomorphic solutions of some differential equations in a Banach space - Gefter, S. L.; Mokrenyuk, V .N. (Журнал математичної фізики, аналізу, геометрії, 2005)
Let A be a bounded operator on a Banach space. A question about the existence of holomorphic solutions of the equation z^2Aw’+g(z)=w is studied. Moreover, general properties of power series of the form ^∞_n=0c_nA^nz^n, c_nC are considered. Mathematics Subject Classification: 34A20, 34A25, 34G10.