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Operator characterizations of Banach lattices with ▫$p$▫-superadditive or ▫$p$▫-subadditive norm
Lavrič, Boris
Naj bosta ▫$E, F$▫ Banachovi mreži in ▫$1\le p\le\infty$▫. Če ▫$F$▫ vsebuje ▫$\ell^n_\infty$▫ enakomerno, potem je vsak pozitiven operator iz ▫$E$▫ v ▫$F$▫ (ali iz ▫$F$▫ v ▫$E$▫) ▫$p$▫-superaditiven ...natanko takrat, ko ima ▫$E$▫ ekvivalentno ▫$p$▫-superaditivno mrežno normo. Dualni rezultat karakterizira Banachove mreže z ekvivalentno ▫$p$▫-subaditivno normo. Dobljeni rezultati omogočajo dokazati obrat Grothendieck-Diestel-Fairesovega izreka o Jordanovi razčlenitvi vektorskih mer z omejenim totalnim razmahom.
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