We say that a Banach space $X$ with a normalized basis
$(e_j)$ has the
Factorization Property if the identity $I:X\to X$ factors through
every operator
$T:X\to X$ with a "large diagonal" (i.e. $\infty_n e^*_n(T(e_n))>0$).
In my talk
I will introduce the notion of Strategically Reproducible Bases, with
the help
of which we identify new spaces with the factorization property, and provide
simplified proofs of the factorization property for spaces, which where
already known
to have this property. This is joint work with Richard Lechner, Pavlos
Motakis, and Paul Müller.