We study which topology have an immediate predecessor in the poset of Sigma(2) of Hausdorff topologies on set X. We show that certain classes of H-closed topologies, do have predecessors. and we give examples of second ...

This article generalizes recent results in the extra invariance for shift-invariant spaces to the context of LCA groups. Let G be a locally compact abelian (LCA) group and K a closed subgroup of G. A closed subspace of ...

The theory of X-normed spaces over non-Archimedean valued fields with valuations of higher rank was introduced by H. Ochsenius and W. H. Schikhof in [1] and further developed in [2–4, 6, 7] and [5]. In order to obtain ...

Let H be Hilbert space and (Ω, m) a σ-finite measure space. Multiplicatively invariant(MI) spaces are closed subspaces of L2(Ω, H) that are invariant under point-wise multiplication byfunctions from a fixed subset of L∞(Ω). ...

Norm Hilbert spaces (NHS) are defined as Banach spaces over valued fields (see 1.4) for which each closed subspace has a norm-orthogonal complement. For fields with a rank I valuation, these spaces were characterized already ...

Se introducen las nociones  de conjunto ω-cerrado, funcion ω-cerrada y espacio P*, generalizando las de conjunto cerrado, función cerrada y espacio P (donde todo Gδ es abierto), respectivamente. Se demuestra que las imágenes ...

We calculate the measure of non-compactness of the multiplication operator Mu acting on non-atomic Köthe spaces. We show that all bounded below multiplication operators acting on Köthe spaces are surjective and therefore ...