Grothendieck’s theorem for absolutely summing multilinear operators is optimal
نویسندگان
چکیده
منابع مشابه
A 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 کاملA Remark on Absolutely Summing Multilinear Mappings *
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 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 کاملA Composition Theorem for Multiple Summing Operators
We prove that the composition S(u1, . . . , un) of a multilinear multiple 2-summing operator S with 2-summing linear operators uj is nuclear, generalizing a linear result of Grothendieck.
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2014
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2013.877013