Biblioteca de la Universidad Complutense de Madrid

A decomposition theorem for polymeasures


Villanueva, Ignacio y Bombal Gordón, Fernando y Pérez García, David (2007) A decomposition theorem for polymeasures. Journal of Mathematical Analysis and Applications, 336 (2). pp. 1316-1323. ISSN 0022-247X

Vista previa

URL Oficial:


We prove that every countably additive polymeasure can be decomposed in a unique way as the sum of a "discrete" polymeasure plus a "continuous" polymeasure. This generalizes a previous result of Saeki.

Tipo de documento:Artículo
Palabras clave:Polymeasures; Multilinear operators; Vector measures power; Series theorem; Multilinear operators; Spaces; Factorization; Algebras
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:11677

R.G. Bartle, N. Dunford, J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955) 289–305.

R.C. Blei, Multilinear measure theory and the Grothendieck factorization theorem, Proc. London Math. Soc. 56 (1988) 529–546.

H.P. Boas, D. Khavinson, Bohr power series theorem in several variables, Proc. Amer. Math. Soc. 125 (1997) 2975–2979.

F. Bombal, M. Fernández, I. Villanueva, Unconditionally converging multilinear operators, Math. Nachr. 226 (2001) 5–15.

F. Bombal, M. Fernández, I. Villanueva, Some classes of multilinear operators on C(K) spaces, Studia Math. 148 (2001) 259–273.

F. Bombal, I. Villanueva, Multilinear operators on spaces of continuous functions, Funct. Approx. Comment. Math. 26 (1998) 117–126.

F. Bombal, I. Villanueva, Integral operators on the product of C(K) spaces, J. Math. Anal. Appl. 264 (2001) 107–121.

A. Defant, D. García, M. Maestre, Bohr's power series theorem and local Banach space theory, J. Reine Angew. Math. 557 (2003) 173–197.

A. Defant, L. Frerick, A logarithmical lower bound for multidimensional Bohr radii, Israel J. Math. 152 (2006) 17–28.

J. Diestel, J.J. Uhl, Vector Measures, Math. Surveys Monogr., vol. 15, Amer. Math. Soc., Providence, RI, 1977.

S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer, 1999. MR1705327 (2001a:46043)

S. Dineen, R.M. Timoney, On a problem of H. Bohr, Bull. Soc. Roy. Sci. Liège 60 (1991) 401–404.

I. Dobrakov, On integration in Banach spaces, VIII (polymeasures), Czechoslovak Math. J. 37 (112) (1987) 487–506.

M. Fernández Unzueta, Unconditionally convergent polynomials in Banach spaces and related properties, Extracta Math. 12 (1997) 305–307.

N. Ghoussoub, W.B. Johnson, Counterexamples to several problems on the factorization of bounded linear operators, Proc. Amer. Math. Soc. 92 (1984) 233–238.

J.E. Gilbert, T. Ito, B.M. Schreiber, Bimeasure algebras on locally compact groups, J. Funct. Anal. 64 (1985) 134–162.

C.C. Graham, B.M. Schreiber, Bimeasure algebras on LCA groups, Pacific J. Math. 115 (1984) 91–127.

A. Grothendieck, Sur les applications linéaires faiblement compactes d'espaces du type C(K) , Canad. J. Math. 5 (1956) 129–173.

J. Gutiérrez, I. Villanueva, Extensions of multilinear operators and Banach space properties, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 1–18.

A. Pelczyński, On weakly compact polynomial operators on B -spaces with Dunford–Pettis property, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 11 (1963) 371–378.

A. Pełczyński, A theorem of Dunford–Pettis type for polynomial operators, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 11 (1963) 371–378.

D. Pérez-García, M.M. Wolf, C. Palazuelos, I. Villanueva, M. Junge, Unbounded violation of tripartite Bell inequalities, preprint. cf.

D. Pérez-García, I. Villanueva, Orthogonally additive polynomials on spaces of continuous functions, J. Math. Anal. Appl. 306 (2005) 97–105.

R.A. Ryan, Dunford–Pettis properties, Bull. Acad. Polon. Sci. Ser. Sci. Math. 27 (1979) 373–379.

S. Saeki, Tensor products of C(X) -spaces and their conjugate spaces, J. Math. Soc. Japan 28 (1976) 33–47.

N.Th. Varopoulos, Tensor algebras and harmonic analysis, Acta Math. 119 (1967) 51–112.

I. Villanueva, Completely continuous multilinear operators on C(K) spaces, Proc. Amer. Math. Soc. 128 (1999)793–801.

K. Ylinen, On vector bimeasures, Ann. Mat. Pura Appl. 117 (1978) 119–138.

Depositado:29 Nov 2010 09:31
Última Modificación:28 Ene 2016 14:49

Sólo personal del repositorio: página de control del artículo