The Fréchet space admits a strictly stronger separable and quasicomplete locally convex topology
Über Quotienten vollständiger topologischer Vektorräume.
Über assoziierte lineare und lokalkonvexe Topologien.
On the associated locally connected space.
A note on the lifting of linear and locally convex topologies on a quotient space.
On the three-space problem and the lifting of bounded sets.
We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining the notion...
A Fréchet Space Which Has a Continuous Norm But Whose Bidual Does Not.
The three-space-problem for locally-m-convex algebras.
We prove that a locally convex algebra A with jointly continuous multiplication is already locally-m-convex, if A contains a two-sided ideal I such that both I and the quotient algebra A/I are locally-m-convex. An application to the behaviour of the associated locally-m-convex topology on ideals is given.
Fréchet spaces of Moscatelli type.
Inductive duals of distinguished frechet spaces
The purpose of this note is to give an example of a distinguished Fréchet space and a non-distinguished Fréchet space which have the same inductive dual. Accordingly, distinguishedness is a property which is not reflected in the inductive dual. In contrast to this example, it was known that the properties of being quasinormable or having the density condition can be characterized in terms of the inductive dual of a Fréchet space.
On a Problem of Bellenot and Dubinsky.
On the spectra of elements in certain algebras of vector valued functions and sequences.
Inductive limits of vector-valued sequence spaces.
Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).
Strong duals of projective limits of (LB)-spaces
We investigate the problem when the strong dual of a projective limit of (LB)-spaces coincides with the inductive limit of the strong duals. It is well-known that the answer is affirmative for spectra of Banach spaces if the projective limit is a quasinormable Fréchet space. In that case, the spectrum satisfies a certain condition which is called “strong P-type”. We provide an example which shows that strong P-type in general does not imply that the strong dual of the projective limit is the inductive...
Semidirect products of locally convex algbras and the three-space-problem.
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