Subspaces in Trace-Valued Spaces with Many Isotropic Vectors

  • Herbert Gross
Part of the Progress in Mathematics book series (PM, volume 1)


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

  1. [0]
    P. Amport, Teilraumverbände in überabzählbar dimensionalen Sesquilinearräumen. Ph.D. Thesis Univ. of Zurich 1978.Google Scholar
  2. [1]
    H. Gross, On Witt’s Theorem in the Denumerably Infinite Case. Math. Ann. 170 (1967) 145–165.CrossRefGoogle Scholar
  3. [2]
    H. Gross, Der euklidische Defekt bei quadratischen Räumen. Math. Ann. 180 (1969) 95–137.CrossRefGoogle Scholar
  4. [3]
    I. Kaplansky, Forms in infinite dimensional spaces. An. Acad. Bras. Ci. 22 (1950) 1–17.Google Scholar
  5. [4]
    E. Witt, Theorie der quadratischen Formen in beliebigen Körpern. J. reine angew. Math. 176 (1937) 31–44.Google Scholar

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Herbert Gross
    • 1
  1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

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