Hypercyclic convolution operators on Fréchet spaces of analytic functions

CARANDO, DANIEL; DIMANT, VERÓNICA; MURO, SANTIAGO

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Año: 2007 vol. 336 p. 1324 - 1340

0022-247X

A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on , which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten–von Neumann class.