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Kohomologija operatorskih algeber : magistrsko deloDolinar, Gregor, 11.08.1971-Delo obravnava zvezno, normalno in popolnoma omejeno Hochschildovo kohomologijo. Najprej opisuje tiste lastnosti operatorskih prostorov in popolnoma omejenih preslikav, ki so potrebne pri ... konstrukciji kohomologije. V prvem poglavju so definirani matrično normirani prostori in operatorski prostori. Dokazan je Ruanov izrek, ki pove, kakšna zveza velja med temi prostori. Obravnavane so tudi nekatere lastnosti in zgledi omenjenih prostorov. V drugem poglavju je najprej dokazan Stinespringov reprezentacijski izrek za linearne popolnoma pozitivne preslikave, nato pa še podoben reprezentacijski izrek za linearne popolnoma omejene preslikave. Tretje poglavje je namenjeno odvajanju in dokazoma, da je odvajanje na ▫$C^*$▫-algebri tako po normi zvezno kot tudi ultrašibko zvezno in da je vsako odvajanje na von Neumannovi algebri notranje. V četrtem poglavju so definirane zvezne in normalne Hochschildove kohomološke grupe.Type of material - master's thesisPublication and manufacture - Ljubljana : [G. Dolinar], 1997Language - slovenianCOBISS.SI-ID - 8443225
Author
Dolinar, Gregor, 11.08.1971-
Other authors
Magajna, Bojan
Topics
matematika |
funkcionalna analiza |
operatorska teorija |
kohomologija |
popolnoma omejene preslikave |
odvajanje |
matrično normirani prostori |
operatorski prostori |
tenzorski produkt |
von Neumannove algebre |
mathematics |
functional analysis |
operator theory |
cohomology |
completely bounded maps |
derivation |
matricially normed spaces |
operator spaces |
tensor product |
von Neumann algebras
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Dolinar, Gregor, 11.08.1971- | 18750 |
Magajna, Bojan | 01470 |
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