Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
38
1
2012
04
01
Non-regularity of multiplications for general measure algebras
265
274
405
EN
J.
Laali
Kharazmi University
M.
Ettefagh
Islamic Azad University
Journal Article
2009
04
30
Let $fM(X)$ be the space of all finite<br /> regular Borel measures on $X$. A general measure algebra is a subspace of<br />$fM(X)$,<br />which is an $L$-space and<br /> has a multiplication preserving the probability measures.<br /> Let $cLsubseteqfM(X)$ be a general measure algebra on a locally<br />compact space<br /> $X$. In this paper, we investigate the relation between Arens<br />regularity of $cL$ and the topology of $X$. We find conditions<br />under which the Arens regularity of $fL$ implies the compactness of $X$.<br />We<br />show that these conditions are necessary.<br />We also present some examples in showing that the new conditions are<br />different from Theorem 3.1 of cite{7}.
http://bims.iranjournals.ir/article_405_227f292f58bd40a514de4597f4abbad2.pdf