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Let E, G be Hausdorff topological vector spaces and let F be a vector space. Assume there is a bilinear operator <.,.> : E X F ?G such that <.,y> : E ?G is continuous for every y £ F. The triple E, F, G is called an abstract duality pair ... see more

Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F? G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i... see more

Let E, F be sets, G an Abelian topological group and b : ExF — G. Then (E, F, G) is called an abstract triple. Let w(F, E) be the weakest toplogy on F such that the maps {b(x, ·): x G E} from F into G are continuous... see more

If ? is a scalar sequence space, a series P Zj in a topological vector space Z is ? multiplier convergent in Z if the series P 8J =1 tj Zj converges in Z for every t = {tj} ? ?-If ? satisfies appropriate conditions, a series in a locally convex space X wh... see more

Let E be a vector valued sequence space with â-dual Åâã. We consider sufficient conditions on E for the series in a pointwise bounded subset of Åâã to be uniformly convergent over certain subsets of E. The conditions involve gliding hump assumpt... see more

Let E be a vector space, F aset, G be a locally convex space, b : E X F — G a map such that ò(-,y): E — G is linear for every y G F; we write b(x, y) = x · y for brevity. Let ? be a scalar sequence space and w(E,F) the weakest topology on E such... see more

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