Maximal Sub Algebras of Group-algebras
نویسنده
چکیده
A closed subalgebra of a Banach algebra is called maximal if it is not contained in any larger proper closed subalgebra. Let G be a discrete abelian topological group and L its group-algebra, i.e. L is the Banach algebra of functions/on G with E*e<J |/(X)| < °° and multiplication defined as convolution. What are the maximal subalgebras of L? The complete answer is not known even when G is the group of integers. Here we assume that G is ordered. Let G+ be the semi-group of nonnegative elements of G and L+ the subset of L consisting of functions which vanish outside of C7+. Then L+ is a proper closed subalgebra of L.
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