Given a real separable Hilbert space H, G(H) denotes the Geometry of the closed linear subspaces of H, S = {E | 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 ∩ F | n belonging to N} when {E} is a convergent sequence and F is a subspace of G(H), and we show that these convergences hold, if this intersection exists. Conversely,...
Two new convergences of closed linear subspaces in the real separable Hilbert space are defined. These are the uniform strong convergence and the simultaneously strong and weak convergence to a single limit. Both convergences are characterized and it is shown that they verify the three axioms of Fréchet.
Given a real separable Hilbert space H, we denote with S = {E(n) | n belongs to N} a sequence of closed linear subspaces of H.
In previous papers, the strong, weak, a--> and b--> convergences are defined and characterized. Now, given a sequence S with strong, weak, a--> or b--> limit, and a linear operator of H, A, the sequence AS is studied.
Given a Hilbert real separable space, H, it is used G(H) to denote the Geometry of the closed linear subspaces of H and S = {E | n ∈ N} a sequence in G(H) (...)
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...
Given a real separable Hilbert space H, we denote with G(H) the geometry of closed linear subspaces of H.
The strong convergence of sequences of subspaces is shown to be a L*-convergence and the weak convergence a L-convergence.
The smallest L*-convergence containing the weak convergence is found, and the orthogonal image of the strong convergence, which is also a L*-convergence, is defined.
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