Copies of lnp’S uniformly in the spaces 2(C [0,1],X) and 1(C [0,1],X)

Autor:	Popa, Dumitru
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles average multiplication operator p-summing linear operators copies of ln p’s uniformly local structure of a Banach space
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	Abstract: We study the presence of copies of ln p ’s uniformly in the spaces 2(C[0, 1],X) and 1(C[0, 1],X). By using Dvoretzky’s theorem we deduce that if X is an infinite- dimensional Banach space, then 2(C[0, 1],X) contains p2-uniformly copies of ln∞’s and 1(C[0, 1],X) contains -uniformly copies of ln 2 ’s for all > 1. As an application, we show that if X is an infinite-dimensional Banach space then the spaces 2(C[0, 1],X) and 1(C[0, 1],X) are distinct, extending the well-known result that the spaces 2(C[0, 1],X) and N(C[0, 1],X) are distinct.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text Full text from SpringerLink