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Characterizing compact Clifford semigroups that embed into convolution and functor-semigroups
Banakh, Taras, 1968- ...
V članku preučujemo algebraične in topološke lastnosti konvolucijskih polgrup verjetnostnih mer na topoloških grupah in dokažemo, da je kompaktna Cliffordova topološka polgrupa ▫$S$▫ vložljiva v ...konvolucijsko polgrupo ▫$P(G)$▫ nad neko topološko grupo ▫$G$▫ tedaj in samo tedaj, ko je ▫$S$▫ vložljiva v polgrupo ▫$\exp(G)$▫ kompaktnih podmnožic grupe ▫$G$▫ tedaj in samo tedaj, ko je ▫$S$▫ inverzna polgrupa in ima 0-dimenzionalno maksimalno polmrežo. Dokažemo tudi, da je takšna Cliffordova polgrupa ▫$S$▫ vložljiva v funktorsko polgrupo ▫$F(G)$▫ nad ustrezno kompaktno topološko grupo ▫$G▫$, za poljuben šibko normalen monadičen funktor ▫$F$▫ v kategoriji kompaktov, za katerega ▫$F(G)$▫ vsebuje ▫$G$▫-invarianten element (ki je analog Haarove mere na ▫$G$▫).
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