Structure of spaces of holomorphic functions on infinite dimensional polydiscs
The paper gives a complete characterization of the subspaces, quotients and complemented subspaces of a stable power series space of infinite type without the assumption of nuclearity, so extending previous work of M. J. Wagner and the author to the nonnuclear case. Various sufficient conditions for the existence of bases in complemented subspaces of infinite type power series spaces are also extended to the nonnuclear case.
Support functionals in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm are completely characterized. An explicit formula for regular support functionals is given. For obtaining a characterization of singular support functionals a generalized Banach limit is applied. Some necessary and sufficient conditions for smooothness of these spaces are given, too.
We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.