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Ocene norm algebraičnih operatorjev v neasociativnih praalgebrah : doktorska disertacijaStrašek, RokV asociativnih Banachovih algebrah obstaja teorija ultrapraalgebeer, ki so definirane z ultrafiltri. Izkaže se, da je definiciji ultrapraalgebre s pomočjo ultrafiltrov, ekvivalentna lastnost ... enakomerne omejenosti algebraičnega operatorja ▫$M_a,b$▫. Teorija je delo nemškega matematika M. Mathieuja. V disertaciji obravnavamo problem oblikovanja sorodne teorije tudi za tiste razrede neasociativnih Banachovih algeber, ki so pomembni predvsem v aplikacijah. Doktorska disertacija je razdeljena v štiri poglavja. V prvem, uvodnem poglavju navedemo kratek pregled zgodovine problema, znanih rezultatovin podamo osnovne definicije pojmov, ki so predmet obravnave naslednjih poglavij. Drugo poglavje je posvečeno razredu enostavnih evklidskihjordanskih algeber. V uvodnem delu je predstavljena njihova klasifikacija, ki temelji na rangu evklidske jordanske algebre. Iz do sedaj objavljenih del je znano, da je jordanske ultrapraalgebre mogoče definirati s pomočjo Jacobson-McCrimmonovega operatorja. V nadaljevanju so podane ocene spektralnih norm Jacobson-McCrimmonovega operatorja v vseh primerih enostavnih jordanskih algeber: IR, Lorentzovih algeber in algeber ustreznih hermitskih matrik, s členi evklidske Hurwitzove algebre. V tretjem poglavju predstavimo Liejeve algebre in v slislu terminologije P. de Harpeja definiramo klasične Banach Liejeve algebre kompaktnih aperatorjev. V njihovem primeru najprej poiščemo ustrezen algebraični operator, nato pa dokažemo njegovo enakomerno omejenost po spektralni normi, v vseh treh razredih: linearnih, ortogonalnih in simplektičnih Liejevih algebrah kompaktnih operatorjev. V četrtem poglavju se posvetimo alternativni algebri realnih oktonionov in njihovim Cayley-Dicksonovim razširitvam. Normo ustreznega algebraičnega operatorja ocenimo po spektralni normi, ki je v realnem primeru kar običajna Hilbertova normaType of material - dissertation ; adult, seriousPublication and manufacture - Maribor : [R. Strašek], 2002Language - slovenianCOBISS.SI-ID - 12086792
Author
Strašek, Rok
Other authors
Zalar, Borut
Topics
Neasociativne praalgebre |
Algebraični operatorji |
Disertacije |
algebra |
kolobarji |
jordanska algebra |
alternativna algebra |
Liejeva algebra |
praalgebra |
ultrapraalgebra |
Banachova algebra |
algebrajska topologija |
disertacije
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Strašek, Rok | 17808 |
Zalar, Borut | 11719 |
Source: Personal bibliographies
and: SICRIS
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