Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 62, No. 1, pp. 73-88 (2005)

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On a completion of prehilbertian spaces

C.-G. Ambrozie

Institute of Mathematics, of the Romanian Academy,
PO Box 1-764, RO-70700 Bucharest -- ROMANIA
E-mail: Calin.Ambrozie@imar.ro

Abstract: We define and study a completion of a prehilbertian space, associated to a family of linear subspaces endowed with linear topologies such that the inclusions are continuous. This provides in particular an orthogonal complement of paraclosed subspaces and an adjoint of paraclosed linear relations.

Keywords: paraclosed subspace; linear relation; operator.

Classification (MSC2000): 46C07, 46C50.; 47A05, 47B99.

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Electronic version published on: 7 Mar 2008.

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