ON LINEAR DYNAMICS OF THE BACKWARD SHIFT OPERATORS

Linear dynamics is a rapidly evolving branch of functional analysis, which was probably born in 1982 with the Toronto PhD thesis of C. Kitai [3]. It has become rather popular, thanks to the efforts of many mathematicians (see [1], [2]). In particular, hypercyclicity and supercyclicity of weighted bilateral shifts were characterized by Salas [4], [5]. In [6] it has been proved that there exists a bounded linear operator satisfying Kitai Criterion on each separable infinite-dimensional Banach space. We are going to study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields.