Kalinin, V. V. On subspaces of a vector space. (Russian) Zbl 0553.46004 Veroyatn. Metody Kibern. 19, 27-29 (1983). Let V be a left vector space over a field. Necessary and sufficient conditions are presented for a class \({\mathcal L}\) of subspaces of V to be the class of all U-closed subspaces for certain total subspace U of the conjugated space \(V^*\). Necessary conditions for the case of a Hilbert space are also obtained. Reviewer: Z.G.Gorgadze MSC: 46A20 Duality theory for topological vector spaces 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis Keywords:left vector space over a field PDFBibTeX XMLCite \textit{V. V. Kalinin}, Veroyatn. Metody Kibern. 19, 27--29 (1983; Zbl 0553.46004) Full Text: EuDML