The inclusion theorem for multiple summing operators
نویسندگان
چکیده
منابع مشابه
A 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 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 کاملLIPSCHITZ p-SUMMING OPERATORS
The notion of Lipschitz p-summing operator is introduced. A non linear Pietsch factorization theorem is proved for such operators and it is shown that a Lipschitz p-summing operator that is linear is a p-summing operator in the usual sense.
متن کاملSumming Inclusion Maps between Symmetric Sequence Spaces
In 1973/74 Bennett and (independently) Carl proved that for 1 ≤ u ≤ 2 the identity map id: `u ↪→ `2 is absolutely (u, 1)-summing, i. e., for every unconditionally summable sequence (xn) in `u the scalar sequence (‖xn‖`2 ) is contained in `u, which improved upon well-known results of Littlewood and Orlicz. The following substantial extension is our main result: For a 2-concave symmetric Banach s...
متن کاملNew Inclusion and Coincidence Theorems for Summing Multilinear Mappings
In this paper we obtain new inclusion and coincidence theorems for absolutely or multiple summing multilinear mappings. In particular, we derive optimal coincidence theorems of Bohnenblust-Hille type for multilinear forms on K-convex Banach spaces of cotype 2.
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: Studia Mathematica
سال: 2004
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm165-3-5