For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that . Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the and topologies on ℋ (U).
We establish Hölder-type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals.
Spaces , , of multipliers of temperate distributions introduced in an earlier paper of the first author are expressed as inductive limits of Hilbert spaces.
We characterize Banach lattices under which each b-weakly compact (resp. b-AM-compact, strong type (B)) operator is L-weakly compact (resp. M-weakly compact).
In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.