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- W3039162806 abstract "Abstract For the spaces , and , we consider the topology of uniform convergence on absolutely convex compact subsets of their (pre‐)dual space. Following the notation of J. Horváth's book we call these topologies κ‐topologies. They are given by a neighbourhood basis consisting of polars of absolutely convex and compact subsets of their (pre‐)dual spaces. In many cases it is more convenient to work with a description of the topology by means of a family of semi‐norms defined by multiplication and/or convolution with functions and by classical norms. We give such families of semi‐norms generating the κ‐topologies on the above spaces of functions and measures defined by integrability properties. In addition, we present a sequence‐space representation of the spaces equipped with the κ‐topology, which complements a result of J. Bonet and M. Maestre. As a byproduct, we give a characterisation of the compact subsets of the spaces , and ." @default.
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- W3039162806 date "2020-07-06" @default.
- W3039162806 modified "2023-10-09" @default.
- W3039162806 title "A simpler description of the κ‐topologies on the spaces DLp,Lp,M1" @default.
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- W3039162806 doi "https://doi.org/10.1002/mana.201900109" @default.
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