Semiperfect semigroups are abelian involution semigroups on which every positive semidefinite function admits a disintegration as an integral of hermitian multiplicative functions. Famous early instances are the group on integers (Herglotz Theorem) and the semigroup of nonnegative integers (Hamburger's Theorem). In the present paper, semiperfect semigroups are characterized within a certain class of semigroups. The paper ends with a necessary condition for the semiperfectness of a finitely generated involution semigroup, a condition which has since been found to be also sufficient.
@article{urn:eudml:doc:41682,
title = {Semiperfect countable C-separative C-finite semigroups.},
journal = {Collectanea Mathematica},
volume = {52},
year = {2001},
pages = {55-73},
zbl = {0996.43008},
mrnumber = {MR1833086},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41682}
}
Bisgaard, Torben Maack. Semiperfect countable C-separative C-finite semigroups.. Collectanea Mathematica, Tome 52 (2001) pp. 55-73. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41682/