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April 2004 Multiple summing operators on C(K) spaces
David Pérez-García, Ignacio Villanueva
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Ark. Mat. 42(1): 153-171 (April 2004). DOI: 10.1007/BF02432914


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.

Funding Statement

Both authors were partially supported by DGICYT grant BMF2001-1284.


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David Pérez-García. Ignacio Villanueva. "Multiple summing operators on C(K) spaces." Ark. Mat. 42 (1) 153 - 171, April 2004.


Received: 1 July 2003; Published: April 2004
First available in Project Euclid: 31 January 2017

zbMATH: 1063.46032
MathSciNet: MR2056549
Digital Object Identifier: 10.1007/BF02432914

Rights: 2004 © Institut Mittag-Leffler


Vol.42 • No. 1 • April 2004
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