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Köthe spaces modeled on spaces of C ∞ functions

Mefharet Kocatepe, Viacheslav Zahariuta (1996)

Studia Mathematica

The isomorphic classification problem for the Köthe models of some C ∞ function spaces is considered. By making use of some interpolative neighborhoods which are related to the linear topological invariant D φ and other invariants related to the “quantity” characteristics of the space, a necessary condition for the isomorphism of two such spaces is proved. As applications, it is shown that some pairs of spaces which have the same interpolation property D φ are not isomorphic.

Linear topological properties of the Lumer-Smirnov class of the polydisc

Marek Nawrocki (1992)

Studia Mathematica

Linear topological properties of the Lumer-Smirnov class L N ∗ ( n ) of the unit polydisc n are studied. The topological dual and the Fréchet envelope are described. It is proved that L N ∗ ( n ) has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for L N ∗ ( n ) .

Linearization and compactness

Jesús Ángel Jaramillo, Ángeles Prieto, Ignacio Zalduendo (2009)

Studia Mathematica

This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping,...

Łojasiewicz ideals in Denjoy-Carleman classes

Vincent Thilliez (2013)

Studia Mathematica

The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the ∞ case have a Denjoy-Carleman counterpart.

Mazur spaces.

Wilansky, Albert (1981)

International Journal of Mathematics and Mathematical Sciences

Measurable functionals on function spaces

J. P. Reus Christensen, J. K. Pachl (1981)

Annales de l'institut Fourier

We prove that all measurable functionals on certain function spaces are measures; this improves the (known) results about weak sequential completeness of spaces of measures. As an application, we prove several results of this form: if the space of invariant functionals on a function space is separable then every invariant functional is a measure.

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