On a class of linear operators.
Stabiliamo teoremi di interpolazione bilineare per una combinazione dei metodi di - e -interpolazione associati ai poligoni, e per il -metodo. Mostriamo che un simile risultato fallisce per il -metodo, e diamo applicazioni all'interpolazione di spazi di operatori.
We study tensor norms and operator ideals related to the ideal , 1 < p < ∞, 0 < σ < 1, of (p,σ)-absolutely continuous operators of Matter. If α is the tensor norm associated with (in the sense of Defant and Floret), we characterize the -nuclear and - integral operators by factorizations by means of the composition of the inclusion map with a diagonal operator , where r is the conjugate exponent of p’/(1-σ). As an application we study the reflexivity of the components of the ideal...
The paper discusses Problems 8 and 88 posed by Stanisław Mazur in the Scottish Book. It turns out that negative solutions to both problems are immediate consequences of the results of Peller [J. Operator Theory 7 (1982)]. We discuss here some quantitative aspects of Problems 8 and 88 and give answers to open problems discussed in a recent paper of Pełczyński and Sukochev in connection with Problem 88.