Título inglés |
On relativization of convergences in G(H). |
Título español |
Sobre relativización de convergencias en G(H). |
Autor/es |
Obras Loscertales y Nasarre, M.ª Carmen de las |
Organización |
Dep. Mat. Fac. Cien. Univ. Oviedo, Oviedo, España |
Revista |
0210-7821 |
Publicación |
1984, 8 (2): 191-197, 8 Ref. |
Tipo de documento |
articulo |
Idioma |
Español |
Resumen inglés |
Given a real separable Hilbert space H, G(H) denotes the Geometry of the closed linear subspaces of H, S = {E(n) | n belonging to N} a sequence of G(H) and [E] the closed linear hull of E. The weak, strong and other convergences in G(H) were defined and characterized in previous papers. Now we study the convergence of sequences {E(n) ∩ F | n belonging to N} when {E(n)} is a convergent sequence and F is a subspace of G(H), and we show that these convergences hold, if this intersection exists. Conversely, given {E(n)} and E, if for each subspace F of G(H) the sequence {E(n) ∩ F} converges to E ∩ F in some one of the forms defined, the sequence {E(n)} converges according to the same type of convergence. |
Clasificación UNESCO |
120214 |
Palabras clave español |
Operadores lineales ; Convergencia ; Sucesiones ; Espacios de Hilbert ; Geometría de subespacios |
Código MathReviews |
MR0783406 |
Código Z-Math |
Zbl 0561.46014 |
Acceso al artículo completo |