Given a real separable Hilbert space H, we denote with G(H) the geometry of closed lineal subspaces of H.
The weak and strong convergence of sequences of subspaces defined in (8) are characterized.
If {E(n) | n ∈ N} is a strong or weak convergent sequence there exists a finite dimensional sequence with the same limit.
The strong convergence is interpreted in terms of nbd-finite family, so that a sequence {E(n) | n ∈ N} is a nbd-finite family if and only if E(n) → 0.
@article{urn:eudml:doc:39841,
title = {Convergencias en G(H).},
journal = {Revista Matem\'atica Hispanoamericana},
volume = {40},
year = {1980},
pages = {177-192},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39841}
}
Obras Loscertales y Nasarre, M.ª Carmen de las. Convergencias en G(H).. Revista Matemática Hispanoamericana, Tome 40 (1980) pp. 177-192. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39841/