Chaotic multipliers on spaces of operators

Alfred Peris¹

Universitat Politècnica de València

We use tensor product techniques to study hypercyclicity and chaos of multipliers defined on certain operator ideals. An operator $T:X \rightarrow X$ on a Banach space $X$ is hypercyclic if there are vectors $x \in X$ whose orbit $\{ x, Tx, T^2x, \dots \}$ is dense in $X$. $T$ is chaotic in the sense of Devaney if, moreover, the set of periodic vectors of $T$ is dense in $X$. We also obtain the first examples of outer multipliers on a Banach algebra which are chaotic.

Footnotes

... Peris¹

joint work with J. Bonet and F. Martınez Giménez