Köthe echelon spaces à la Dieudonné

On Köthe Sequence Spaces and Linear Logic

We present a category of locally convex topological vector spaces which is a model of propositional classical linear logic, based on the standard concept of Köthe sequence spaces. In this setting, the “of course” connective of linear logic has a quite simple structure of commutative Hopf algebra. The co-Kleisli category of this linear category is a cartesian closed category of entire mappings. ...

Besov – Köthe Spaces and Applications Kwok -

We introduce and study the family of Besov–Köthe spaces which is a generalization of the Besov spaces, the Besov–Morrey spaces and the variable Besov spaces. As an application of the general results for the Besov–Köthe spaces, we identify a pre-dual of the Besov–Morrey space.

Echelon Spaces of Order »

The notion of Echelon spaces was introduced by Köthe [2] as a means of constructing sequence spaces by taking the intersection of multiples of I1 (see below for definitions). The definition was extended by Dieudonné and Gomes [l] to include lp for \^p< °o. It is the purpose of this note to consider the case, p = co. AH of the terminology defined below is due to Köthe. A sequence of complex numb...

Contribution à l'étude de la maladie athéromateuse

Metrizable Köthe Spaces1

The sets A = A(r) and A*=A(A) are vector lattices, [l], and are called associated Köthe spaces. Initially Köthe and Toeplitz, [9], and later Köthe, in a series of papers of which [lO] is representative, studied these spaces for the case where E is the space of natural numbers with the discrete topology and p(n) = 1 for every natural number w. Dieudonné, [4], extended the theory to the case for ...