The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed subspace of $c_0$ [2]. This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring compactly through $\ell^p$-spaces ($1\leq p < \infty$) were studied by many authors (see [1] and the references therein). In this talk, even though hypercyclic operators are not compact, we consider operator ideals generated by hypercyclic backward weighted shifts and examine their factorization properties.

Joint work with Yunied Puig.

[1] J. H. Fourie, Injective and surjective hulls of classical p-compact operators with applications to unconditionally p-compact operators, Studia Math., 240 (2018), 147--159.

[2] T. Terzio\u{g}lu, A characterization of compact linear mappings, Arch. Math. 22 (1971), 76-78.