Norm attaining and numerical radius attaining operators.

Título inglés	Norm attaining and numerical radius attaining operators.
Título español	Operadores que alcanzan la norma y el radio numérico.
Autor/es	Acosta, María D. ; Payá, Rafael
Organización	Dep. Anál. Mat. Fac. Cienc. Secc. Mat. Univ. Granada, Granada, España
Revista	0214-3577
Publicación	1989, 2 (SUPL.): 19-25, 18 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result by C. Stegall where it is assumed the the dual space Y* has the Radon-Nikodým property to obtain a stronger assertion. Numerical radius attaining operators behave in a quite similar way. It is also true that the set of operators on an arbitrary Banach space whose adjoints attain their numerical radii is norm-dense in the space of all operators. However no example is known of a Banach space such that the numerical radius attaining operators on are not dense. We can prove that such space must fail the Radon-Nikodým property. The content of this paper is merely expository. Complete proofs will published elsewhere.
Clasificación UNESCO	120201
Palabras clave español	Operadores ; Espacios de Banach ; Propiedad de Radon-Nikodym
Código MathReviews	MR1057204
Código Z-Math	Zbl 0722.47009
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