Quasi-splitting subspaces and Foulis-Randall subspaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F11%3A33116597" target="_blank" >RIV/61989592:15310/11:33116597 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.3668124" target="_blank" >http://dx.doi.org/10.1063/1.3668124</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.3668124" target="_blank" >10.1063/1.3668124</a>

Result language
angličtina
Original language name
Quasi-splitting subspaces and Foulis-Randall subspaces
Original language description
For a pre-Hilbert space S, let F(S) denote the orthogonally closed subspaces, Eq(S) the quasi-splitting subspaces, E(S) the splitting subspaces, D(S) the Foulis-Randall subspaces, and R(S) the maximal Foulis-Randall subspaces, of S. It was an open problem whether the equalities D(S) = F(S) and E(S) = R(S) hold in general [Cattaneo, G. and Marino, G., "Spectral decomposition of pre-Hilbert spaces as regard to suitable classes of normal closed operators," Boll. Unione Mat. Ital. 6 1-B, 451-466 (1982); Cattaneo, G., Franco, G., and Marino, G., "Ordering of families of subspaces of pre-Hilbert spaces and Dacey pre-Hilbert spaces," Boll. Unione Mat. Ital. 71-B, 167-183 (1987); Dvurečenskij, A., Gleason's Theorem and Its Applications (Kluwer, Dordrecht, 1992), p. 243.]. We prove that the first equality is true and exhibit a pre-Hilbert space S for which the second equality fails.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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