Journal of the
Korean Mathematical Society JKMS

We give conditions so that a polynomial be factorable through an $L_r(\mu)$ space. Among them, we prove that, given a Banach space $X$ and an index $m$, every absolutely summing operator on $X$ is $1$-factorable if and only if every $1$-dominated $m$-homogeneous polynomial on $X$ is right $1$-factorable, if and only if every $1$-dominated $m$-homogeneous polynomial on $X$ is left $1$-factorable. As a consequence, if $X$ has local unconditional structure, then every $1$-dominated homogeneous polynomial on $X$ is right and left $1$-factorable.

Keywords: right $r$-factorable polynomial, left $r$-factorable polynomial, $p$-dominated polynomial

MSC numbers: Primary 46G25; Secondary 47H60