On relativization of convergences in G(H).

Autores: María Carmen de las Obras Loscertales y Nasarre
Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 8, Nº. 2, 1984, págs. 191-197
Idioma: español
Títulos paralelos:
- Sobre relativización de convergencias en G(H).
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Resumen
- 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) 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) n F} converges to E n F in some one of the forms defined, the sequence {E(n)} converges according to the same type of convergence.