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Structure theory of power series spaces of infinite type.

Dietmar Vogt (2003)

RACSAM

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 and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm

Henryk Hudzik, Yi Ning Ye (1990)

Commentationes Mathematicae Universitatis Carolinae

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.

Tame Köthe Sequence Spaces are Quasi-Normable

Krzysztof Piszczek (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that every tame Fréchet space admits a continuous norm and that every tame Köthe sequence space is quasi-normable.

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