Multiple summing operators on C(K) spaces

David Pérez-García; Ignacio Villanueva

doi:10.1007/BF02432914

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Home > Journals > Ark. Mat. > Volume 42 > Issue 1 > Article

April 2004 Multiple summing operators on C(K) spaces

David Pérez-García, Ignacio Villanueva

Author Affiliations +

David Pérez-García,¹ Ignacio Villanueva¹
¹Departamento de Análisis Matemático Facultad de Matemáticas, Universidad Complutense de Madrid

Ark. Mat. 42(1): 153-171 (April 2004). DOI: 10.1007/BF02432914

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Abstract

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. https://doi.org/10.1007/BF02432914