Locally Bounded Noncontinuous Linear Forms on Strong Duals of Nondistinguished Köthe Echelon Spaces
نویسندگان
چکیده
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.
منابع مشابه
Duals and approximate duals of g-frames in Hilbert spaces
In this paper we get some results and applications for duals and approximate duals of g-frames in Hilbert spaces. In particular, we consider the stability of duals and approximate duals under bounded operators and we study duals and approximate duals of g-frames in the direct sum of Hilbert spaces. We also obtain some results for perturbations of approximate duals.
متن کاملON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES
The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...
متن کاملOn the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences
The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...
متن کاملFrames and Homogeneous Spaces
Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...
متن کاملVariants of the Maurey-Rosenthal theorem for quasi Köthe function spaces
The Maurey-Rosenthal theorem states that each bounded and linear operator T from a quasi normed space E into some L p (ν) (0 < p < r < ∞) which satisfies a vector-valued norm inequality
متن کامل