A space of vector-valued measures and a strict topology

Zafarani, J.

doi:10.1007/bf01165782

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1987

2010

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“…There is an extensive literature on this subject; see, for example, [10,11]. Also, for such a study in another context, see [4,14,16], for example. For a generalization of the strict topology and/or strict topology in a more general setting, see, for example, [2,7].…”

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confidence: 99%

The Strict Topology on the Discrete Lebesgue Spaces

Maghsoudi

Nasr-Isfahani²

2010

Bull. Aust. Math. Soc.

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Let be a set and σ be a positive function on . We introduce and study a locally convex topology β 1 ( , σ ) on the space 1 ( , σ ) such that the strong dual of ( 1 ( , σ ), β 1 ( , σ )) can be identified with the Banach space (c 0 ( , 1/σ ), · ∞,σ ). We also show that, except for the case where is finite, there are infinitely many such locally convex topologies on 1 ( , σ ). Finally, we investigate some other properties of the locally convex space ( 1 ( , σ ), β 1 ( , σ )), and as an application, we answer partially a question raised by A. I. Singh ['L ∞ 0 (G) * as the second dual of the group algebra L 1 (G) with a locally convex topology', Michigan Math. J. 46 (1999), 143-150].

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