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Multiple summing operators on C(k) spaces

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2004-04
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Springer Verlag
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In this paper, we characterize, for 1 ≤ p <∞, the multiple (p, 1)-summing multilinear operators on the product of C(K) spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of (p, 1)-summing linear operators on C(K) in terms of their representing measures and a new multilinear characterization of L∞ spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H.P. Rosenthal and S.J. Szarek and give new results about polymeasures.
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