Abstract
When one has to handle two mutually perpendicular subspaces F and G in a sesquilinear space (E,Φ) it is often a great advantage if E splits orthogonally such that F and G are contained in summands,
If this happens then we say that F and G can be orthogonally separated in E .
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References to Chapter VI
L. Brand, Erweiterung von algebraischen Isometrien in sesquilinearen Räumen. PhD Thesis, Univ. of Zurich 1974.
F.K. Fischer, Orthogonale und symplektische Zerlegung sesquilinearer Räume. Master’s Thesis, Univ. of Zurich 1977.
A. Frapolli, Generalizzazione di un teorema di H.A. Keller sulla modularità del reticolo dei sottospazi ortogonalmente chiusi di uno spazio sesquilineare. Master’s Thesis, Univ. of Zurich 1975. (This concerns some technicalities when char k = 2; in [6] it is assumed that char k 2.)
H. Gross and P. Hafner, The sublattice of an orthogonal pair in a modular lattice. Ann. Acad. Sci. Fenn. vol. 4 1978/1979.
B. Jonsson, Distributive sublattices of a modular lattice. Proc. Amer. Math. Soc. 6 (1955) 682–688.
H.A. Keller, Ueber den Verband der orthogonal abgeschlossenen Teilräume eines hermiteschen Raumes. Letter to the author of Nov. 7, 1973, pp. 1–6.
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Gross, H. (1979). Orthogonal and Symplectic Separation. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1454-8_7
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DOI: https://doi.org/10.1007/978-1-4757-1454-8_7
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