Algebre z ločljivim spektrom in Banachovimi moduli nad njimi : doktorska disertacija
Bračič, Janko
Naj bo ▫$\mathfrak{A}$▫ komutativna Banachova algebra z enoto. Kakšen mora biti levi Banachov ▫$\mathfrak{A}$▫-modul ▫$\mathcal{X}$▫, da vsak element iz ▫$\mathfrak{A}$▫ inducira na ▫$\mathcal{X}$▫ ...dekomponibilen operator? Da lahko odgovorimo na to vprašanje, izdelamo za module teprijo upodobitev, ki razširja teorijo upodobitev algeber. Vpeljano je veliko pojmov, ki na naraven način razširjajo pojme iz teorije algeber na module. Tako, na primer, definiramo module z ločljivim spektrom in odgovor se glasi: če je ▫$\mathcal{X}$▫, takšen levi Banachov ▫$\mathfrak{A}$▫-modul, da ima njegov dualni modul ▫${\mathcal X}^\ast$▫ ločljiv spekter , potem vsak element iz ▫$\mathfrak{A}$▫ inducira na ▫$\mathcal{X}$▫ dekomponilen operator množenja. Teorija upodobitev modulov nam omogoča, da vpeljemo razred enostavnih multiplikatorjev na danem Banachovem modulu. Na primer, vsak multiplikator na polenostavni Banachovi algebri je enostaven. Za omenjeni razred multiplikatorjev pokažemo, da imajo podobne lastnosti kot multiplikatorji na algebrah. Če modul na katerem delamo, zadošča nekaterim dodatnim pogojem, potem je množica vseh enostavnih multiplikatorjev na njem polenostavna komutativna Banachova algebra z enoto. S pomočjo tega lahko izpeljemo trditve, ki so analogne znanim rezultatom o multiplikatorjih na polenostavnih Banachovih algebrah.
Type of material - dissertation
; adult, serious
Publication and manufacture - Ljubljana : [J. Bračič], 2001
Central Technological Library of the University of Ljubljana
52047/1316 Skladišče IN: 320020225
available - outside loan, loan period: 14 days
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