On equivalent conditions to quasi-perfectness of abelian *-semigroups.

Nobuhisa Sakakibara

Displaying similar documents to “On equivalent conditions to quasi-perfectness of abelian *-semigroups.”

Stieltjes perfect semigroups are perfect

Torben Maack Bisgaard, Nobuhisa Sakakibara (2005)

Czechoslovak Mathematical Journal

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An abelian $*$ -semigroup $S$ is perfect (resp. Stieltjes perfect) if every positive definite (resp. completely so) function on $S$ admits a unique disintegration as an integral of hermitian multiplicative functions (resp. nonnegative such). We prove that every Stieltjes perfect semigroup is perfect. The converse has been known for semigroups with neutral element, but is here shown to be not true in general. We prove that an abelian $*$ -semigroup $S$ is perfect if for each $s \in S$ there exist $t \in S$ and $m, n \in ℕ_{0}$ ...