Bornological spaces of type
We study in terms of corresponding Köthe matrices when every continuous linear operator between two Köthe spaces is bounded, the consequences of the existence of unbounded continuous linear operators, and related topics.
Characterizations of pairs (E,F) of complete (LF)?spaces such that every continuous linear map from E to F maps a 0?neighbourhood of E into a bounded subset of F are given. The case of sequence (LF)?spaces is also considered. These results are similar to the ones due to D. Vogt in the case E and F are Fréchet spaces. The research continues work of J. Bonet, A. Galbis, S. Önal, T. Terzioglu and D. Vogt.
In this paper we generalize some results concerning bounded variation functions on sequence spaces.