Ultrastability of ideals of homogeneous polynomials and multilinear mappings on Banach spaces

Using the theory of full and symmetric tensor norms on normed spaces, a theorem of Kürsten and Heinrich on ultrastability and maximality of normed operator ideals is extended to ideals of $n$-homogeneous polynomials and $n$-linear mappings--scalar-valued and vector-valued. The motivation for these results is the following important special case: the ``uniterated'' Aron-Berner extension $\overline{q}^{\mathfrak U}$: $E'' \longrightarrow F''$ of an $n$-homogeneous polynomial $q: E\longrightarrow F$ to the bidual remains in certain ideals under preservation of the norm. Moreover, Lotz's characterization of maximal normed ideals of linear mappings through appropriate tensor norms is proved for ideals of $n$-homogeneous scalar-valued polynomials and ideals of $n$-linear mappings.