We give necessary and sufficient conditions for the sum of subspaces H 1,…, H n , n ≥ 2, of a Hilbert space H to be a subspace and present various properties of the n-tuples of subspaces with closed sum.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 10, pp. 1381–1425, October, 2011.
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Feshchenko, I.S. On closeness of the sum of n subspaces of a Hilbert space. Ukr Math J 63, 1566–1622 (2012). https://doi.org/10.1007/s11253-012-0601-9
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DOI: https://doi.org/10.1007/s11253-012-0601-9