On cotype and a Grothendieck-type theorem for absolutely summing multilinear operators
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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In this note we obtain new coincidence theorems for absolutely summing multilinear mappings between Banach spaces. We also prove that our results, in general, can not be improved.
متن کاملA General Extrapolation Theorem for Absolutely Summing Operators
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 < ∞...
متن کاملOn the Multilinear Extensions of the Concept of Absolutely Summing Operators
The core of the theory of absolutely summing operators lie in the ideas of A. Grothendieck in the 1950s. Further work (after a decade) of A. Pietsch [19] and Lindenstrauss and Pe l czyński [9] clarified Grothendiecks insights and nowadays the ideal of absolutely summing operators is a central topic of investigation. For details on absolutely summing operators we refer to the book by Diestel-Jar...
متن کاملAbsolutely Summing Operators on Non Commutative C-algebras and Applications
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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ژورنال
عنوان ژورنال: Quaestiones Mathematicae
سال: 2011
ISSN: 1607-3606,1727-933X
DOI: 10.2989/16073606.2011.640747