Best approximation in vector valued function spaces
Archivos
Autores
Khalil, Roshdi
Director
Tipo de contenido
Artículo de revista
Idioma del documento
EspañolFecha de publicación
1985
Título de la revista
ISSN de la revista
Título del volumen
Documentos PDF
Resumen
Let T be the unit circle, and m be the normalized Lebesgue measure on T. If H is a separable Hilbert space, we let L∞T,H) be the space of essentially bounded functions on T with values in H. Continuous functions with values in H are denoted by C(T,H), and H∞(T,H) is the space of bounded holomorphic functions in the unit disk with values in H. The object of this paper is to prove that (H∞+C)(T,H) is proximinal in L∞(T,H). This generalizes the scalar valued case done by Axler, S. et al. We also prove that (H∞+C)(T,l∞) |H∞(T,l∞) is an M-ideal of L∞(T,l∞) | H∞ (T, l∞), and V(T,l∞) is an M-ideal of L∞(T, l∞)whenever V is an M-ideal of L∞, where V(T,l∞) {g ϵ L∞(T,l∞): and lt;g(t), δn and gt; ϵ V for all n}.