 

M. Akbari Tootkaboni
Lmccompactification of a semitopological semigroup as a space of eultrafilters view print


Published: 
October 20, 2013 
Keywords: 
Semigroup Compactification, Lmccompactification, zfilter, efilter 
Subject: 
22A20, 54D80 


Abstract
Let S be a semitopological semigroup and CB(S)
denote the C*algebra of all bounded complex valued continuous
functions on S with uniform norm. A function f∈ CB(S) is left multiplicative continuous
if and only if T_{μ}f∈ CB(S) for all μ in the spectrum of CB(S),
where T_{μ}f(s)=μ(L_{s}f) and L_{s}f(x)=f(sx) for each s,x∈ S.
The collection of all the left multiplicative continuous functions on S is denoted by Lmc(S).
In this paper, the Lmccompactification of a semitopological semigroup S is reconstructed as a space of eultrafilters.
This construction is applied to obtain some algebraic properties of (ε ,S^{Lmc}), such that S^{Lmc} is the
spectrum of Lmc(S), for semitopological semigroups S. It is shown that if S is a locally compact
semitopological semigroup, then S*=S^{Lmc} \ ε(S) is a left ideal
of S^{Lmc} if and only if for each x,y∈ S, there exists a compact zero set A containing x such that
{t∈S : yt∈A} is a compact set.


Author information
Department of Mathematics, Shahed University, Tehran, Iran
akbari@shahed.ac.ir

