Abstract
The classical Theorem of Witt says that any isometry T0: F → F̄ between finite dimensional subspaces F, F̄ of a non degenerate tracevalued space (E, Φ) can be extended to an isometry T: E → E ([4], Satz 4 and Anmerkung p. 31).
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References to Chapter V
P. Amport, Teilraumverbände in überabzählbar dimensionalen Sesquilinearräumen. Ph.D. Thesis Univ. of Zurich 1978.
H. Gross, On Witt’s Theorem in the Denumerably Infinite Case. Math. Ann. 170 (1967) 145–165.
H. Gross, Der euklidische Defekt bei quadratischen Räumen. Math. Ann. 180 (1969) 95–137.
I. Kaplansky, Forms in infinite dimensional spaces. An. Acad. Bras. Ci. 22 (1950) 1–17.
E. Witt, Theorie der quadratischen Formen in beliebigen Körpern. J. reine angew. Math. 176 (1937) 31–44.
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© 1979 Springer Science+Business Media New York
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Gross, H. (1979). Subspaces in Trace-Valued Spaces with Many Isotropic Vectors. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3542-7_6
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DOI: https://doi.org/10.1007/978-1-4899-3542-7_6
Publisher Name: Birkhäuser, Boston, MA
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