Spaces of absolutely summing polynomials
نویسندگان
چکیده
منابع مشابه
A Note on Scalar-valued Absolutely Summing Homogeneous Polynomials between Banach Spaces
In this note we show that the well known coincidence results for scalar-valued homogeneous polynomials can not be generalized in some natural directions.
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w,q = supφ∈BX́ ( ∑k j=1 | φ(xj) | ) 1 q . This is a natural generalization of the concept of (p; q)-summing operators and in the last years has been studied by several authors. The infimum of the L > 0 for which the inequality holds defines a norm ‖.‖as(p;q) for the case p ≥ 1 or a p-norm for the case p < 1 on the space of (p; q)-summing homogeneous polynomials. The space of all m-homogeneous (p...
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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...
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.
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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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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2007
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-15041