On relativization of convergences in G(H).

M.ª Carmen de las Obras Loscertales y Nasarre

Stochastica (1984)

  • Volume: 8, Issue: 2, page 191-197
  • ISSN: 0210-7821

Abstract

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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.

How to cite

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Obras Loscertales y Nasarre, M.ª Carmen de las. "Sobre relativización de convergencias en G(H).." Stochastica 8.2 (1984): 191-197. <http://eudml.org/doc/39013>.

@article{ObrasLoscertalesyNasarre1984,
author = {Obras Loscertales y Nasarre, M.ª Carmen de las},
journal = {Stochastica},
keywords = {Operadores lineales; Convergencia; Sucesiones; Espacios de Hilbert; Geometría de subespacios; geometry of the closed linear subspaces; convergences of sequences},
language = {spa},
number = {2},
pages = {191-197},
title = {Sobre relativización de convergencias en G(H).},
url = {http://eudml.org/doc/39013},
volume = {8},
year = {1984},
}

TY - JOUR
AU - Obras Loscertales y Nasarre, M.ª Carmen de las
TI - Sobre relativización de convergencias en G(H).
JO - Stochastica
PY - 1984
VL - 8
IS - 2
SP - 191
EP - 197
LA - spa
KW - Operadores lineales; Convergencia; Sucesiones; Espacios de Hilbert; Geometría de subespacios; geometry of the closed linear subspaces; convergences of sequences
UR - http://eudml.org/doc/39013
ER -

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