On the spectral radius of positive operators on Banach sequence spaces
Drnovšek, Roman, 1966- ; Peperko, Aljoša
Naj bodo ▫$K_1, \ldots , K_n$▫ (neskončne) nenegativne matrike, ki definirajo omejene operatorje na danem Banachovem prostoru zaporedij. Za dano funkcijo ▫$n$▫ spremenljivk ▫$f \colon [0,\infty) ...\times \ldots \times [0,\infty) \to [0,\infty)$▫ definiramo nenegativno matriko ▫$\hat{f} (K_1, \ldots , K_n)$▫ in obravnavamo neenakost ▫$$r(\hat{f} (K_1, \ldots , K_n)) \leqslant \frac{1}{n} (r(K_1)+ \ldots +r(K_n)),$$▫ kjer z ▫$r$▫ zaznamujemo spektralni radij. Najdemo največjo funkcijo ▫$f$▫, za katero ta neenakost velja za vse ▫$K_1, \ldots , K_n$▫. Izpeljemo tudi neskočnorazsežno razširitev Cohen-ovega rezultata, da je spektralni radij konveksna funkcija diagonalnih elementov nenegativne matrike.
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