Title of article :
Integral mappings between Banach spaces
Author/Authors :
Ignacio Villanueva 1، نويسنده ,
Issue Information :
دوهفته نامه با شماره پیاپی سال 2003
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.
2003 Elsevier Science (USA). All rights reserved.
Keywords :
Spaces of continuous functions , Integral operators , multilinear operators , Injective tensor product
Journal title :
Journal of Mathematical Analysis and Applications
Journal title :
Journal of Mathematical Analysis and Applications