On some geometric properties of certain Köthe sequence spaces

On Some Geometric Properties of Certain Köthe Sequence Spaces

It is proved that if a Köthe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS(X) > 1, then X is order continuous. It is shown that a weakly sequentially complete Köthe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( ⊕∞ i=1 Xi)Φ of a sequence of Banach sp...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Some Geometric Properties of Sequence Spaces Involving Lacunary Sequence

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. ...

Some p -Type New Sequence Spaces and Their Geometric Properties

and Applied Analysis 3 of the space λA is defined by λA {f : f g ◦ A; g ∈ λ′}. Let X be a seminormed space. A set Y ⊂ X is called fundamental set if the span of Y is dense in X. An application of HahnBanach theorem on fundamental set is as follows: if Y is the subset of a seminormed space X and f Y 0 implies f 0 for f ∈ X′, then Y is a fundamental set see 11 . By the idea mentioned above, let u...