Abstract
In this paper, we characterize, for 1≤p<∞, the multiple (p, 1)-summing multilinear operators on the product ofC(K) spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of (p, 1)-summing linear operators onC(K) in terms of their representing measures and a new multilinear characterization ofL ∞ 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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Both authors were partially supported by DGICYT grant BMF2001-1284.
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Pérez-García, D., Villanueva, I. Multiple summing operators onC(K) spaces. Ark. Mat. 42, 153–171 (2004). https://doi.org/10.1007/BF02385583
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DOI: https://doi.org/10.1007/BF02385583