Quadratic forms and sesquilinear forms in infinite dimensional spaces. Witt type theorems in spaces of denumerably infinite dimension

Herbert Gross

Mémoires de la Société Mathématique de France (1976)

  • Volume: 48, page 21-33
  • ISSN: 0249-633X

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Gross, Herbert. "Quadratic forms and sesquilinear forms in infinite dimensional spaces. Witt type theorems in spaces of denumerably infinite dimension." Mémoires de la Société Mathématique de France 48 (1976): 21-33. <http://eudml.org/doc/94737>.

@article{Gross1976,
author = {Gross, Herbert},
journal = {Mémoires de la Société Mathématique de France},
language = {eng},
pages = {21-33},
publisher = {Société mathématique de France},
title = {Quadratic forms and sesquilinear forms in infinite dimensional spaces. Witt type theorems in spaces of denumerably infinite dimension},
url = {http://eudml.org/doc/94737},
volume = {48},
year = {1976},
}

TY - JOUR
AU - Gross, Herbert
TI - Quadratic forms and sesquilinear forms in infinite dimensional spaces. Witt type theorems in spaces of denumerably infinite dimension
JO - Mémoires de la Société Mathématique de France
PY - 1976
PB - Société mathématique de France
VL - 48
SP - 21
EP - 33
LA - eng
UR - http://eudml.org/doc/94737
ER -

References

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  1. [1] W. ALLENSPACH, Erweiterung von Isometrien in alternierenden Räumen, Zürich University Thesis 1973. 
  2. [2] G. BIRKHOFF, Lattice Theory, AMS Providence, Rhode Island, 1973. 
  3. [3] N. BOURBAKI, Eléments de Mathématiques, Algèbre Chap. IX, Formes sesquilinéaires et formes quadratiques, Hermann, Paris, 1959. 
  4. [4] L. BRAND, Erweiterung von algebraischen Isometrien in sesquilinearen Räumen. Zürich University Thesis 1974. 
  5. [5] A. FRÖHLICH, Quadratic forms à la local theory. Proc. Camb. Phil. Soc. (1967), 63, 579-586. Zbl0153.05701MR35 #5389
  6. [6] H. GROSS, Sesquilinear forms and quadratic forms in infinite dimensional spaces, Vol. 1 : Spaces of countably infinite dimension. To appear. Zbl0356.15021
  7. [7] H. GROSS, Der Euklidische Defekt bei quadratischen Räumen, Math. Ann. 180, 95-137 (1969). Zbl0162.04302MR39 #6823
  8. [8] H. GROSS, On Witt's Theorem in the denumerably infinite case, Math. Ann. 170, 145-165 (1967). Zbl0153.05601MR34 #5848
  9. [9] H. GROSS and H.R. FISCHER, Quadratic Forms and linear topologies I, Math. Ann. 157, 296-325 (1964). Zbl0142.00403MR30 #3149
  10. [10] I. KAPLANSKY, Forms in infinite-dimensional spaces, Ann. Acad. Bras. Ci. 22, 1-17 (1950). MR12,238a
  11. [11] H.A. KELLER, On the lattice of all closed subspaces of a Hermitean Space, Rev. Soc. Mat. Chile, Vol. 2 (1976). 
  12. [12] S. LANG, On quasi algebraic closure, Ann. of Math. (1952) 55, 373-390. Important improvements can be found in M. Nagata : Note on a paper of Lang concerning quasi algebraic closure. Mem. Univ. Kyoto Ser. A 30 (1957) 237-241. For further developments and references see G. Terjanian : Dimension arithmétique d'un corps. Journ. of Algebra 22 (1972) 517-545 ; further G. Maxwell : A note on Artin's Diophantine Conjecture. Canad. Math. Bull. (1970) 13, 119-120. Zbl0046.26202
  13. [13] F. MAEDA and S. MAEDA, Theory of Symmetric Lattices, Springer NY 1970. Zbl0219.06002MR44 #123
  14. [14] U. SCHNEIDER, Beiträge zur Theorie der sesquilinearen Räume unendlicher Dimension. Zürich University Thesis 1975. 

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