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may 2016 More on the locally convex space $(M(X),\beta(X))$ of a locally compact Hausdorff space $X$
Hossein Javanshiri, Rasoul Nasr-Isfahani
Bull. Belg. Math. Soc. Simon Stevin 23(2): 191-201 (may 2016). DOI: 10.36045/bbms/1464710113

Abstract

In the previous paper [12] we introduced the definition of the strict topology $\beta(X)$ on the measure space $M(X)$ for a locally compact Hausdorff space $X$. In this paper, we consider on $M(X)$ the topology $\beta(X)$ and we show that $\beta(X)$ is the weak topology under all left multipliers induced by a function space on $M(X)$. We then show that $\beta(X)$ 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 $(M(X),\beta(X))$ is a Mazur space and the locally convex space $(M(S),\beta(S))$, equipped with the convolution multiplication is a complete semitopological algebra, for a wide class of locally compact semigroups $S$.

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Hossein Javanshiri. Rasoul Nasr-Isfahani. "More on the locally convex space $(M(X),\beta(X))$ of a locally compact Hausdorff space $X$." Bull. Belg. Math. Soc. Simon Stevin 23 (2) 191 - 201, may 2016. https://doi.org/10.36045/bbms/1464710113

Information

Published: may 2016
First available in Project Euclid: 31 May 2016

zbMATH: 1354.46028
MathSciNet: MR3507077
Digital Object Identifier: 10.36045/bbms/1464710113

Subjects:
Primary: 28C05 , 28C15 , 46A03 , 46H05

Keywords: compactly cancellative semigroup , locally compact Hausdorff space , locally convex topology , Mazur space , semitopological algebra , strict topology

Rights: Copyright © 2016 The Belgian Mathematical Society

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Vol.23 • No. 2 • may 2016
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