Locally bounded noncontinuous linear forms on strong duals of nondistinguished Köthe echelon spaces

Locally Bounded Noncontinuous Linear Forms on Strong Duals of Nondistinguished Köthe Echelon Spaces

In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K C which is locally bounded (i.e. bounded on the bounded sets) but not continuous. It is also shown that every nondistinguished Kothe echelon space contains a sectional subspace with a particular structure.

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. ...

Locally Uniformly Convex Norms in Banach Spaces and Their Duals

It is shown that a Banach space with locally uniformly convex dual admits an equivalent norm that is itself locally uniformly convex.

Bounded generators of linear spaces

on the effect of linear & non-linear texts on students comprehension and recalling

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