A mixed topology over the space of measures with continuous translations on a locally compact semigroup

Maghsoudi, S.

doi:10.1007/s00233-012-9395-1

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…An argument similar to the proof of [19,Theorem 2.2] with the aid of Proposition 2.2 gives the following generalization of that Theorem. Theorem 2.3.…”

Section: Proposition 22 Let X Be a Locally Compact Hausdorff Space Then The Topology β(X) On M(x) Is The Mixed Topologymentioning

confidence: 88%

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More on the locally convex space $(M(X),\beta(X))$ of a locally compact Hausdorff space $X$

Javanshiri¹,

Nasr-Isfahani²

2016

Bull. Belg. Math. Soc. Simon Stevin

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In the previous paper [12] we introduced the definition of the strict topology β(X) on the measure space M(X) for a locally compact Hausdorff space X. In this paper, we consider on M(X) the topology β(X) and we show that β(X) is the weak topology under all left multipliers induced by a function space on M(X). We then show that β(X) can be considered as a mixed topology. This result is not only of interest in its own right, but also it paves the way to prove that (M(X), β(X)) is a Mazur space and the locally convex space (M(S), β(S)), equipped with the convolution multiplication is a complete semitopological algebra, for a wide class of locally compact semigroups S. Introduction and preliminariesAbout sixty years passed since two mathematicians introduced two new topologies with different methods. Over the years a considerable amount of work has been done on them and on similar topologies by functional analysts. One of them, Buck [7], investigated the space of continuous functions with the strict topology and the other one, the Polish mathematician Alexiewicz [4], considered a vector space E on which two norms are given and defined a notion of convergence of sequences in E, which, in some sense, mixed the topologies given by the two norms. These methods have been studied and generalized by several mathematicians as, for example, Aguayo and his coauthors in [1,2,3], Collins [10], Kua [18],

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“…An argument similar to the proof of [19,Theorem 2.2] with the aid of Proposition 2.2 gives the following generalization of that Theorem. Theorem 2.3.…”

Section: Proposition 22 Let X Be a Locally Compact Hausdorff Space Then The Topology β(X) On M(x) Is The Mixed Topologymentioning

confidence: 88%

“…Choi and Kim [8], Cobzas [9], Katsaras [13,14,15,16], Malkowsky and Velickovic [22], Taylor and his coauthor [23,24], Wiweger [25,26] and [12,19,20,21]. Now, let M(X) be the Banach space of all complex Radon measures on the locally compact Hausdorff space X with the total variation norm.…”

mentioning

confidence: 99%