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Regular multilinear operators on C(K) spaces

Published online by Cambridge University Press:  17 April 2009

Fernando Bombal
Affiliation:
Departamento de Análisis MatemáticoUniversidad Complutense de Madrid28040 MadridSpain
Ignacio Villanueva
Affiliation:
Departamento de Análisis MatemáticoUniversidad Complutense de Madrid28040 MadridSpain
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Abstract

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The purpose of this paper is to characterise the class of regular continuous multilinear operators on a product of C(K) spaces, with values in an arbitrary Banach space. This class has been considered recently by several authors in connection with problems of factorisation of polynomials and holomorphic mappings. We also obtain several characterisations of a compact dispersed space K in terms of polynomials and multilinear forms defined on C(K).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Alaminos, J., Choi, Y.S., Kim, S.G., and Payá, R., ‘Norm attaining bilinear forms on spaces of continuous functions’, (preprint).Google Scholar
[2]Aron, R., Choi, S.Y., and Llavona, J.L.G., ‘Estimates by polynomials’, Bull. Austral. Math. Soc. 52 (1995), 475486.CrossRefGoogle Scholar
[3]Aron, R. and Galindo, P., ‘Weakly compact multilinear mappings’, Proc. Edinburgh Math. Soc. 40 (1997), 181192.CrossRefGoogle Scholar
[4]Bombal, F. and Villanueva, I., ‘Multilinear operators on spaces of continuous functions’, Funct. Approx. Comment. Math. 25 (1998), 117126.Google Scholar
[5]Diestel, J. and Uhl, J.J., Vector measures, Mathematical Surveys 15 (American Math. Soc., Providence, R.I., 1977).CrossRefGoogle Scholar
[6]Dobrakov, I.On integration in Banach spaces, VIII (polymeasures), Czech. Math. J. 37 (1987), 487506.CrossRefGoogle Scholar
[7]Dobrakov, I., ‘Representation of multilinear operators on x C 0(Ti)’, Czech. Math. J. 39 (1989), 288302.CrossRefGoogle Scholar
[8]González, M. and Gutiérrez, J., ‘Factorisation of weakly continuous holomorphic mappings’, Studia Math. 118 (1996), 117133.Google Scholar
[9]González, M. and Gutiérrez, J., ‘Injective factorisation of holomorphic mappings’ (to appear).Google Scholar
[10]Holub, J.R., ‘Tensor product bases and tensor diagonals’, Trans. Amer. Math. Soc. 151 (1970), 563579.CrossRefGoogle Scholar
[11]Pelczynski, A., ‘A theorem of Dunford-Pettis type for polynomial operators’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 11 (1963), 379386.Google Scholar
[12]Pelczynsky, A. and Semadeni, Z., ‘Spaces of continuous functions (III). Spaces C(ω) for ω without perfect subsets’, Studia Math. 18 (1959), 211222.CrossRefGoogle Scholar
[13]Ruess, W. and Werner, D., ‘Structural properties of operator spaces’, Acta Univ. Carotin. – Math. Phys. 28 (1987), 127136.Google Scholar
[14]Villanueva, I., ‘Polimedidas y representatión de operadores multilineales de C1X 1) x … x Cd, Xd)’, Tesina de Licenciatura, Dpto. de Análisis Matemático, Fac. de Matemáticas, Universidad Complutense de Madrid (1997).Google Scholar