On the existence of non-norm-attaining operators
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadatos
Título
On the existence of non-norm-attaining operatorsFecha de publicación
2021-07-09Editor
Cambridge University PressISSN
1474-7480; 1475-3030Cita bibliográfica
Dantas, S., Jung, M., & Martínez-Cervantes, G. (2023). ON THE EXISTENCE OF NON-NORM-ATTAINING OPERATORS. Journal of the Institute of Mathematics of Jussieu, 22(3), 1023-1035. doi:10.1017/S1474748021000311Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in L(E,F)
. By using a theorem due to Pfitzner on James boundaries, we show that if there exists a ... [+]
In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in L(E,F)
. By using a theorem due to Pfitzner on James boundaries, we show that if there exists a relatively compact set K of L(E,F)
(in the weak operator topology) such that 0
is an element of its closure (in the weak operator topology) but it is not in its norm-closed convex hull, then we can guarantee the existence of an operator that does not attain its norm. This allows us to provide the following generalisation of results due to Holub and Mujica. If E is a reflexive space, F is an arbitrary Banach space and the pair (E,F)
has the (pointwise-)bounded compact approximation property, then the following are equivalent:
(i) K(E,F)=L(E,F)
;
(ii) Every operator from E into F attains its norm;
(iii) (L(E,F),τc)∗=(L(E,F),∥⋅∥)∗
,
where τc
denotes the topology of compact convergence. We conclude the article by presenting a characterisation of the Schur property in terms of norm-attaining operators. [-]
Publicado en
J. Inst. Math. Jussieu (2023), 22(3), 1023–1035Derechos de acceso
© The Author(s), 2021. Published by Cambridge University Press.
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
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