Publication:
Continuous multilinear operators on C(K) spaces and polymeasures

dc.contributor.authorBombal Gordón, Fernando
dc.date.accessioned2023-06-20T10:33:13Z
dc.date.available2023-06-20T10:33:13Z
dc.date.issued2007
dc.descriptionProceedings of "Banach space theory: classical topics and new directions, Cáceres 2006". (Satellite conference of the World Congress ICM2006, Madrid 2006)
dc.description.abstractThis paper is a survey of the results of Bombal and I. Villanueva Díez [Funct. Approx. Comment. Math. 26 (1998), 117–126; Bombal, D. Pérez-García and Villanueva Díez [Q. J. Math. 55 (2004), no. 4, 441–450; and Pérez-García and Villanueva Díez [Ark. Mat. 42 (2004), no. 1, 153–171; The results surveyed concern Riesz-type integral representations of continuous multilinear operators on C(K) -spaces by polymeasures.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMTM
dc.description.sponsorshipUCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/20142
dc.identifier.citationAlencar, R., Matos, M.C., “Some Classes of Multilinear Mappings between Banach Spaces”, Publicaciones del Departamento de Análisis Matemático de la U.C.M., Sec. 1, No. 12. Madrid, 1989. Aron, R.M., Berner, P.D., A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. France 106 (1978), 3 – 24. Blei, R., Multilinear measure theory and the Grothendieck factorization theorem, Proc. of the London Math. Soc., 56 (1988), 529 – 546. Blei, R., “Analysis in Integer and Fractional Dimensions”, Cambridge University Pres, 2001. Bombal, F.,Alexander Grothendieck’s work on Functional Analysis, in “Advanced Courses of Mathematical Analysis. Proceedings of the second International School”, M. V. Velasco and A. Rodr´ıguez-Palacios, Eds., World Scientific Publishing Co., Singapore, 2007, 16 – 36. Bombal, F., Fernández, M., Villanueva, I., Unconditionally converging multilinear operators, Math. Nachr., 226 (2001), 5 – 15. Bombal, F., Fernández, M., Villanueva, I., Some classes of multilinear operators on C(K) spaces, Studia Math., 148 (3) (2001), 259 – 273. Bombal, F., Villanueva, I., Multilinear operators on spaces of continuous functions, Funct. et Approx., XXVI (1998), 117 – 126. Bombal, F., Villanueva, I., Regular multilinear operators on C(K) spaces, Bull. Austral. Math. Soc., 60 (1999), 11 – 20. Bombal, F., Villanueva, I., Integral operators on the product of C(K)spaces, J. Math. Anal. Appl., 264 (2001), 107 – 121. Bombal, F.,Pérez-García, D., Villanueva, I., Multilinear extensions of Grothendieck’s theorem, Quart. J. Math., 55 (2004), 441 – 450. Clarkson, J.A., Adams, C.R., On definition of bounded variation for functions of two variables, Trans. Amer. Math. Soc., 35 (1933), 824 – 854. Davie, A.M., Quotient algebras of uniform algebras. J. London Math. Soc., 7 (1973), 31 – 40. Diestel, J., Jarchow, H., Tonge, A., “Absolutely Summing Operators”, Cambridge Univ. Press, 1995. Diestel, J., Uhl, J.J., “Vector Measures”, A.M.S. Math. Surveys, Vol. 15, Providence, R.I., 1977. Dobrakov, I., On integration in Banach spaces, VIII (polymeasures), Czech. Math. J., 37 (112) (1987), 487 – 506. Dobrakov, I., Representation of Multilinear Operators on ×C0(Ti), Czech. Math. J., 39 (114) (1989), 288 – 302. Fréchet, M., Sur les fonctionnelles bilin´eaires, Trans. Amer. Math. Soc., 16 (1915), 215 – 234. González, M., Gutiérrez, J.M., Unconditionally converging polynomials in Banach spaces, Math. Proc. Cambridge Phil. Soc., 117 (1995), 321 –331. Gutiérrez, J., Villanueva, I., Extension of multilinear operators and Banach space properties, Proc. Roy. Soc. Edimb. Ser. A, 133 A (2003), 1 – 18. Grothendieck, A., Sur les applications linéaires faiblement compactes d’espaces du type C(K), Canadian J. Math., 5 (1953), 129 – 173. Johnson, G., Woodward, G., On p-Sidon sets, Indiana Univ. Math. J., 24 (1974), 161 – 167. Karni, S., Merzbach, E., On the extension of bimeasures, J. Anal. Math., 55 (1990), 1 – 16. Littlewood, J.E., On bounded bilinear forms in an infinite number of variables, Quart. J. Math. Oxford, 1 (1930), 164 – 174. Matos, M.C., Fully absolutely summing and Hilbert-Schmidt multilinear mappings, To appear in Collect. Math. Pelczynski, A., On Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Pol. Sci., 10 (1962), 641 – 648. Pelczynski, A., A theorem of Dunford-Pettis type for polynomial operators, Bull. Acad. Pol. Sci., 11 (1963), 379 – 386. Pérez-García, D., Operadores multilineales absolutamente sumantes, Tesina, Universidad Complutense de Madrid, 2002. Pérez-García, D., The inclusion theorem for multiple summing operators, Studia Math., 165 (2004), 275 – 290. Pérez-García, D., Villanueva, I., Multiple summing operators on Banach spaces, J. of Math. Anal. and Appl., 285 (2003), 86 – 96. Pérez-García, D., Villanueva, I., Multiple summing operators on C(K) spaces, Ark.Math., 42 (2004), 153 – 171. Pietsch, A., Ideals of multilinear functionals (design of a theory), in “Proceedings of the 2nd. International Conference on Operator Algebras, Ideals and their Applications in Theoretical Physics”, Leipzig, Teubner-Texte, 1983, 185 – 199. Riesz, F., Sur les opérations fonctionnelles linéaires, C. R. Acad. Sci. Paris, 149 (1909), 974 – 977. Rudin, W., “Real and Complex Analysis”, McGraw-Hill, 1970. Villanueva, I., “Representación de Operadores Multilineales en Espacios de Funciones Continuas”, Thesis, U.C.M., Madrid, 1999. Villanueva, I., Completely continuous multilinear operators on C(K) spaces, Proc. Amer. Math. Soc., 128 (1999), 793 – 801. Villanueva, I., Some results concerning polymeasures. Rev. Acad. Ci. de Madrid, 94 (2001), 455 – 460. Ylinen, K., On vector bimeasures, Ann. Mat. Pura Appl. (4) 117 (1978), 115 – 138.
dc.identifier.issn0213-8743
dc.identifier.officialurlhttp://www.eweb.unex.es/eweb/extracta/Vol-22-2/22P2Bomba-congreso.pdf
dc.identifier.relatedurlhttp://www.eweb.unex.es/eweb/extracta/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/50476
dc.issue.number2
dc.journal.titleExtracta Mathematicae
dc.language.isoeng
dc.page.final146
dc.page.initial127
dc.publisherUniversidad de Extremadura, Departamento de Matemáticas
dc.relation.projectID2005-0082
dc.relation.projectID9103456
dc.rights.accessRightsrestricted access
dc.subject.cdu517.983.2
dc.subject.keywordmultilinear operators
dc.subject.keywordpolymeasures
dc.subject.ucmAnálisis funcional y teoría de operadores
dc.titleContinuous multilinear operators on C(K) spaces and polymeasures
dc.typejournal article
dc.volume.number22
dspace.entity.typePublication
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