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Subspaces in Hermitean spaces of countable dimension. (English) Zbl 0517.46016


MSC:

46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
11E10 Forms over real fields
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References:

[1] Allenspach, W.: Erweiterung von Isometrien in alternierenden Räumen. Ph. D. Thesis, University of Zürich 1973
[2] Bäni, W.: Subspaces of positive definite inner product spaces of countable dimension. Pacific J. Math.82, 1-14 (1979) · Zbl 0387.15017
[3] Bäni, W.: Inner product spaces of infinite dimension; on the lattice method. Arch. Math. (Basel)33, 338-347 (1979) · Zbl 0411.15014
[4] Bäni, W., Gross, H.: On SAP fields. Math. Z.162, 69-74 (1978) · Zbl 0379.15014 · doi:10.1007/BF01437824
[5] Birkhoff, G.: Lattice Theory 3rd ed. Providence: Amer. Math. Soc. 1973
[6] Bognár, J.: Indefinite Inner Product Spaces. Ergeb. Math. Grenzgeb.78. Berlin-Heidelberg-New York: Springer 1974
[7] Brand, L.: Erweiterung von algebraischen Isometrien in sesquilinearen Räumen. Ph. D. Thesis, University of Zürich 1974
[8] Gabriel, P.: Représentations indécomposables. Séminaire Bourbaki Exposé 444. Lecture Notes in Math.431. Berlin-Heidelberg-New York: Springer 1975
[9] Gross, H.: Pn Witt’s Theorem in the denumerably infinite case. Math. Ann.170, 145-165, (1967) · Zbl 0153.05601 · doi:10.1007/BF01350674
[10] Gross, H.: Eine Bemerkung zu dichten Unterräumen reeller quadratischer Räume. Comment. Math. Helv.45, 472-493 (1970) · Zbl 0287.15009 · doi:10.1007/BF02567345
[11] Gross, H.: Isomorphisms between lattices of linear subspaces which are induced by isometries. J. Algebra49, 537-546 (1977) · Zbl 0387.15018 · doi:10.1016/0021-8693(77)90257-5
[12] Gross, H.: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Math.1, Boston-Basel-Stuttgart: Birkhäuser 1979 · Zbl 0413.10013
[13] Jónsson, B.: Distributive sublattices of a modular lattice. Proc. Amer. Math. Soc.6, 682-688 (1955) · Zbl 0066.28301
[14] Kaplansky, I.: Forms in infinite dimensional spaces. An. Acad. Brasil. Ci.22, 1-17 (1950) · Zbl 0038.07002
[15] Köthe G.: Topological Vector Spaces I. Berlin-Heidelberg-New York: Springer 1969
[16] Maxwell, G.: Classification of countably infinite hermitean forms over skew fields. Amer. J. Math.96, 145-155 (1974) · Zbl 0306.15009 · doi:10.2307/2373585
[17] Moresi, R.: Untersuchungen in abzählbar-dimensionalen nicht spurwertigen ?-hermiteschen Räumen. Ph. D. Thesis, University of Zürich 1980
[18] Prestel, A.: Remarks on the Pythagoras and Hasse number of real fields. J. Reine Angew. Math.303/304, 284-294 (1978) · Zbl 0396.10013 · doi:10.1515/crll.1978.303-304.284
[19] Quebbemann, H. G., Scharlau, R., Scharlau, W., Schulte, M.: Quadratische Formen in additiven Kategorien. Bull. Soc. Math. France48, 93-101 (1976) · Zbl 0352.18018
[20] Quebbermann, H. G., Scharlau, W., Schulte, M.: Quadratic and hermitean forms in additive and abelian categories. J. Algebra59, 264-289 (1979) · Zbl 0412.18016 · doi:10.1016/0021-8693(79)90126-1
[21] Schneider, U.: Beiträge zur Theorie der sesquilinearen Räume unendlicher Dimensionen. Ph. D. Thesis, University of Zürich 1975
[22] Witt, E.: Theorie der quadratischen Formen in beliebigen Körpern. J. Reine Angew. Math.176, 31-44 (1937) · Zbl 0015.05701 · doi:10.1515/crll.1937.176.31
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