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.
@article{urn:eudml:doc:39013,
title = {Sobre relativizaci\'on de convergencias en G(H).},
journal = {Stochastica},
volume = {8},
year = {1984},
pages = {191-197},
zbl = {0561.46014},
mrnumber = {MR0783406},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39013}
}
Obras Loscertales y Nasarre, M.ª Carmen de las. Sobre relativización de convergencias en G(H).. Stochastica, Tome 8 (1984) pp. 191-197. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39013/