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DC Field | Value | Language |
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dc.contributor.author | Buhagiar, David | - |
dc.contributor.author | Chetcuti, Emanuel | - |
dc.contributor.author | Weber, Hendrik | - |
dc.date.accessioned | 2017-04-15T18:29:31Z | - |
dc.date.available | 2017-04-15T18:29:31Z | - |
dc.date.issued | 2008-09 | - |
dc.identifier.citation | Buhagiar, D., Chetcuti, E., & Weber, H. (2008). Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces. Journal of Mathematical Analysis and Applications, 345(2), 725-730. | en_GB |
dc.identifier.uri | https://www.um.edu.mt/library/oar//handle/123456789/18309 | - |
dc.description.abstract | Let S be a pre-Hilbert space. We study quasi-splitting subspaces of S and compare the class of such subspaces, denoted by Eq(S), with that of splitting subspaces E(S). In [D. Buhagiar, E. Chetcuti, Quasi splitting subspaces in a pre-Hilbert space, Math. Nachr. 280 (5–6) (2007) 479–484] it is proved that if S has a non-zero finite codimension in its completion, then Eq(S) = E(S). In the present paper it is shown that if S has a total orthonormal system, then Eq(S) = E(S) implies completeness of S. In view of this result, it is natural to study the problem of the existence of a total orthonormal system in a pre-Hilbert space. In particular, it is proved that if every algebraic complement of S in its completion is separable, then S has a total orthonormal system. | en_GB |
dc.language.iso | en | en_GB |
dc.publisher | Elsevier | en_GB |
dc.rights | info:eu-repo/semantics/openAccess | en_GB |
dc.subject | Inner product spaces | en_GB |
dc.subject | Invariant subspaces | en_GB |
dc.subject | Completeness theorem | en_GB |
dc.title | Orthonormal bases and quasi-splitting subspaces in pre-Hilbert spaces | en_GB |
dc.type | article | en_GB |
dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
dc.description.reviewed | peer-reviewed | en_GB |
dc.identifier.doi | 10.1016/j.jmaa.2008.04.024 | - |
Appears in Collections: | Scholarly Works - FacSciMat |
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