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13.
Analiza. Del 3, Riccatijeva enačba v algebrah z involucijo
Dobovišek, Mirko
Naloga obravnava stabilizabilnost in popolno stabilizabilnost para elementov ▫$C^*$▫-algebre ter obstoj sebiadjungiranih rešitev algebrajske Riccatijeve enačbe ▫$-xcc^*x+b^*x+xb+a=0$▫ in ...klasifikacijo njenih rešitev. Dokazano je, da je par elementov ▫$C^*$▫-algebre stabilizabilen v ▫$B(H)$▫ natanko tedaj, ko je stabilizabilen v ▫$C^*$▫-algebri v kateri so koeficienti. Za popolno stabilizabilnost so poiskani štirje ekvivalentni pogoji. Dokazanih je več izrekov o eksistenci sebi adjungiranih rešitev tako v ▫$C^*$▫-algebri kot v lokalno ▫$C^*$▫-algebri. Dokazano je tudi, da je v primeru ▫$C^*$▫-algebre in v primeru lokalno C*-algebre množica rešitev v bijektivni korespondenci s točno določenimi idempotenti. S tem je posplošen izrek J.C.Willemsa in W.A.Coppela z algeber matrik na lokalno ▫$C^*$▫-algebre.
Type of material - research report
Publication and manufacture - Ljubljana : Inštitut za matematiko, fiziko in mehaniko, 1991
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