×

Operators with common hypercyclic subspaces. (English) Zbl 1106.47010

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.

MSC:

47A16 Cyclic vectors, hypercyclic and chaotic operators

Citations:

Zbl 0999.47009
PDFBibTeX XMLCite