Publication: Integral mappings between Banach spaces
Loading...
Full text at PDC
Publication Date
2003
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
We consider the classes of “Grothendieck-integral” (G-integral)and “Pietsch-integral” (P-integral) linear and multilinear operators (see definitions below), and we prove that a multilinear operator between Banach spaces is G-integral (resp. P-integral) if and only if its linearization is G-integral (resp. P-integral) on the injective tensor product of the spaces, together with some related results concerning certain canonically associated linear operators. As an application we give a new proof of a result on the Radon-Nikodym property of the dual of the injective tensor product of Banach spaces. Moreover, we give a simple proof of a characterization of the G-integral operators on C(K,X) spaces and we also give a partial characterization of P-integral operators on C(K,X) spaces.
Description
UCM subjects
Unesco subjects
Keywords
Citation
R. Alencar, Multilinear mappings of nuclear and integral type, Proc. Amer. Math. Soc. 94 (1985) 33–38.
R. Alencar, On reflexivity and basis for P( m E) , Proc. Roy. Irish Acad. 85A (1985) 131–138.
F. Bombal, Medidas vectoriales y espacios de funciones continuas, Publicaciones del Departamento de Análisis Matemático, Fac. de Matemáticas, Universidad Complutense de Madrid, 1984.
F. Bombal, I. Villanueva, Integral operators on C(K) spaces, J. Math. Anal. Appl., to appear. cf.
A. Defant, K. Floret, Tensor Norms and Operator Ideals, in: North-Holland Math. Studies, Vol. 176, 1993.
J. Diestel, H. Jarchow, A. Tonge, Absolutely Summing Operators, in: Cambridge Stud. Adv. Math., Vol. 43, Cambridge Univ. Press, Cambridge, 1995.
J. Diestel, J.J. Uhl, Vector Measures, in: Mathematical Surveys, Vol. 15, American Mathematical Society, Providence, RI, 1977.
T. Figiel, W.B. Johnson, The approximation property does not imply the bounded approximation property, Proc. Amer. Math. Soc. 41 (1973) 197–200.
A. Grothendieck, Produits tensoriels topologiques et espaces nucláires, Mem. Amer. Math. Soc. 16 (1955).
H.E. Lacey, The Isometric Theory of Classical Banach Spaces, Springer, Berlin, 1974.
S.J. Montgomery-Smith, P. Saab, p -Summing operators on injective tensor products of spaces, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 283–296.
C.P. Stegall, J.R. Retherford, Fully nuclear and completely nuclear operators with applications to L 1 - and L ∞ -spaces, Trans. Amer. Math. Soc. 163 (1972) 457–492.
W.M. Ruess, C.P. Stegall, Extreme points in duals of operator spaces, Math. Ann. 261 (1982) 535–546.
P. Saab, Integral operators on spaces of continuous vector-valued measures, Proc. Amer. Math. Soc. 111 (1991) 1003–1013.