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Sobre relativización de convergencias en G(H).

M.ª Carmen de las Obras Loscertales y Nasarre (1984)

Stochastica

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,...

Some more weak Hubert spaces

Alec Edgington (1991)

Studia Mathematica

We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace.

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