Positive p-summing operators, vector measures and tensor products
نویسندگان
چکیده
منابع مشابه
p-Summing Operators on Injective Tensor Products of Spaces
Let X, Y and Z be Banach spaces, and let ∏ p(Y, Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T : X⊗̂ǫY −→ Z is 1-summing if and only if a naturally associated operator T : X −→ ∏ 1(Y, Z) is 1-summing. This result need not be true if X is not a £∞-space. For p > 1, several examples are given with X = C[0, 1] t...
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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.
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In this note, a nonlinear version of the Extrapolation Theorem is proved and as a corollary, a nonlinear version of the Grothendieck’s Theorem is presented. Finally, we prove that if T : X → H is Lipschitz with X being a pointed metric space and T (0) = 0 such that T∣H∗ is q-summing (1 ≤ q <∞), then T is Lipschitz 1-summing.
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A number of mathematicians have considered the problem of writing an operator as a product of \nice" operators, such as positive, hermitian or normal operators. Our principal reference for this is a paper of P.Y. Wu 6], but see also 2] and 5]. This kind of question, and related questions, have also been considered in a C*-algebra context, see 3]. A core result of Wu's paper is his theorem that ...
متن کاملA remark on p-summing norms of operators
In this paper we improve a result of W. B. Johnson and G. Schechtman by proving that the p-summing norm of any operator with n-dimensional domain can be well-approximated using C(p)n logn(log logn)2 vectors if 1 < p < 2, and using C(p)np/2 logn if 2 < p <∞. 1. p-summing norms Throughout this paper we will follow notations of N. Tomczak-Jaegermann [To]. Definition 1.1. Let X and Y be Banach spac...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1988
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500003291