Non-regularity of multiplications for general measure algebras

Document Type : Research Paper


1 Kharazmi University

2 Islamic Azad University


Let $fM(X)$ be the  space of  all finite
 regular Borel measures on $X$. A general measure algebra is a subspace  of
which is an $L$-space and
 has a multiplication preserving the probability measures.
 Let $cLsubseteqfM(X)$ be a general measure algebra on a locally
compact space
 $X$. In this paper, we investigate the relation between Arens
regularity of $cL$ and the topology of $X$. We  find conditions
under which the Arens regularity of $fL$ implies the compactness of $X$.
show that these conditions are necessary.
We also  present some examples in showing that the new conditions are
different from  Theorem 3.1 of cite{7}.