Polynomially compact derivations on Banach algebras
Brešar, Matej ; Turovskii, Yuri
Obravnavamo zvezno odvajanje ▫$D$▫ na Banachovi algebri ▫$\mathcal{A}$▫ z lastnostjo, da je ▫$p(D)$▫ is kompakten operator za nek polinom ▫$p$▫. Pokažemo, da ima bodisi ▫$\mathcal{A}$▫ končno ...razsežen ideal, ki ni vsebovan v radikalu ▫${\mathrm{rad}}(\mathcal{A})$▫ algebre ▫$\mathcal{A}$▫, ali pa obstaja tak nadaljnji polinom ▫$\tilde{p}$▫, da ▫$\tilde{p} (D)$▫ slika ▫$\mathcal{A}$▫ v ▫${\mathrm{rad}}(\mathcal{A})$▫. Posebni primer, ko je ▫$D^n$▫ kompakten, je obravnavan podrobneje.
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