Título:
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Multilinear operators on spaces of continuous functions
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Autores:
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Villanueva, Ignacio ;
Bombal Gordón, Fernando
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Tipo de documento:
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texto impreso
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Editorial:
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Faculty of Mathematics and Computer Science of Adam Mickiewicz University, 1998
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis funcional y teoría de operadores
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Tipo = Artículo
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Resumen:
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Let E1, . . . ,Ed be Banach spaces such that all linear operators from Ei into E_j (i 6= j) are weakly compact. The authors show that every continuous d-linear operator T on E1 × • • • × Ed to a Banach space F possesses a unique bounded multilinear extension T__ : E__ 1 × • • • × E__ d ! F__ that is !_ ? !_-separately continuous and kT__k = kTk. In particular, existence of unique continuous multilinear extensions from C(K1)ו • •× C(Kd) (Ki – Hausdorff compact spaces) to C(K1)__ו • •×C(Kd)__ that are separately weak_-continuous is established. As a corollary, integral representations with respect to polymeasures for multilinear mappings on C(K1)ו • •×C(Kd) into a Banach space are found. The results generalize a theorem due to Pelczynsky about multilinear extensions from C(K1) × • • • × C(Kd) to the Cartesian product of the spaces of bounded Baire functions on Ki.
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En línea:
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https://eprints.ucm.es/id/eprint/12357/1/1998Multioperators.pdf
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