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On the weak convergences and their topologies. (Spanish. English summary) Zbl 0658.46015

Given a real separable Hilbert space H, we denote with G(H) the geometry of the closed linear spaces of H, with \(S=\{E^{(n)}| n\in N\}^ a \)sequence in G(H) and with [C] the closed linear hull of the set C. In previous papers we have defined and characterized the weak convergence in G(H), \(E^{(n)}\rightharpoonup E\), \(E^{(n)}\rightharpoonup^{a}E\), \(E^{(n)}\rightharpoonup^{b}E\). Now we report a topological characterization of these convergences by the weak topology \(\tau_ W\) and the finest topology with the weak convergence, \(\tau_ C\).

MSC:

46C99 Inner product spaces and their generalizations, Hilbert spaces
06C20 Complemented modular lattices, continuous geometries
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