Aron, R.; Bès, J.; Léon, F.; Peris, A. Operators with common hypercyclic subspaces. (English) Zbl 1106.47010 J. Oper. Theory 54, No. 2, 251-260 (2005). The authors show that a family of operator acting on a common Banach space may fail to support a common hypercyclic subspace, even if each operator in the family has a hypercyclic subspace. Also, it is shown that if the family is uncountable, it may even fail to have single common hypercyclic vector. The present paper extends a result of F. León–Saavedra and A. Montes–Rodríguez [J. Funct.Anal.148, No. 2, 524–545 (1997; Zbl 0999.47009)] by providing a reasonable sufficient condition on a countable family of hypercyclic operators acting on a Banach space to have a common infinite-dimensional hypercyclic subspace. Reviewer: Ömer Gök (Istanbul) Cited in 13 Documents MSC: 47A16 Cyclic vectors, hypercyclic and chaotic operators Keywords:hypercyclic vectors; hypercyclic operators; hereditarily universal families; separable Banach space Citations:Zbl 0999.47009 PDFBibTeX XMLCite \textit{R. Aron} et al., J. Oper. Theory 54, No. 2, 251--260 (2005; Zbl 1106.47010)