Elementarni operatorji na Calkinovi algebri in von Neumann-Schattenovih razredih : doktorska disertacija
Magajna, Bojan
Naj bo ▫${\cal H}$▫ Hilbertov prostor in ▫${\cal B(H)}$▫ algebra vseh omejenih linearnih operatorjev na njem. V prvem delu disertacije raziskujemo sistem enačb ▫$$\sum_{j=1}^m X_jA_iY_j = B_i,\quad ...i=1,...,r$$▫ kjer so ▫$A_i$▫ in ▫$B_i$▫ znani, ▫$X_j$▫ in ▫$Y_j$▫ pa neznani elementi algebre ▫${\cal B(H)}$▫. V primeru ▫$m=r$▫ podamo potreben in zadosten pogoj, ki mu morajo zadoščati operatorji ▫$A_i$▫, da bo gornji sistem rešljiv pri poljubnih ▫$B_i \in {\cal B(H)}$▫. Dobljeni rezultat (katerega milejša oblika velja tudi v splošnejših Banachovih algebrah z enim samim maksimalnim idealom) je uporaben pri proučevanju vprašanja, kdaj je zaloga vrednosti danega elementarnega operatorja vsebovana v kakem idealu algebre ▫${\cal B(H)}$▫. Kot posledico spoznamo, da na Calkinovi algebri ni neničelnih kompaktnih elementarnih operatorjev. Drugi del naloge se omejuje na posebne primere elementarnih operatorjev, predvsem na t.i. posplošena odvajanja. Med drugim pokažemo, kako se izraža bistveni numerični zaklad zožitve posplošenega odvajanja na Hilbert-Schmidtov razred ▫$C^2({\cal H})$▫ z numeričnima in bistvenima numeričnima zakladoma operatorjev, ki ga inducirata. Nadalje opredelimo subnormalna in kvazinormalna posplošena odvajanja na ▫$C^2({\cal H})$▫.
Type of material - dissertation
Publication and manufacture - Ljubljana : [B. Magajna], 1985
Central Technological Library of the University of Ljubljana
52047/528 Skladišče IN: 398501289
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