Absolutely summing linear operators into spaces with no finite cotype
نویسندگان
چکیده
منابع مشابه
Cotype and Non Linear Absolutely Summing Mappings
In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every n-linear mapping from L∞-spaces into K is (2; 2, ..., 2,∞)-summing and also shown that every n-linear mapping from L∞-spaces into F is (q; 2, ..., 2)-summing whenever F has cotype q. We also give new examples of analytic summing mappings and polynomial...
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The notion of absolutely (p; q)-summing linear operators is due to A. Pietsch [18] and B. Mitiagin and A. Pe lczyński [14], inspired by previous works of A. Grothendieck. The nonlinear theory of absolutely summing operators was initiated by A. Pietsch and a complete nonlinear approach was introduced by M.C. Matos [12]. Let X,Y be Banach spaces over a fixed scalar field K = R or C; for 1 ≤ p < ∞...
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Let E be a Banach space that does not contain any copy of l and A be a non commutative C∗-algebra. We prove that every absolutely summing operator from A into E∗ is compact, thus answering a question of Pe lczynski. As application, we show that if G is a compact metrizable abelian group and Λ is a Riesz subset of its dual then every countably additiveA∗-valued measure with bounded variation and...
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A linear and continuous operator between Banach spaces is said to be absolutely summing if it maps unconditionally convergent series into absolutely convergent series. Moreover, it improves properties of stochastic processes. Indeed, N.Ghoussoub in [7] proved that an operator is absolutely summing if and only if it maps amarts (asymptotic martingales) into uniform amarts. In this paper we go a ...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2009
ISSN: 1370-1444
DOI: 10.36045/bbms/1244038147