# Quadratic Forms in Infinite Dimensional Vector Spaces

Book

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

1. Front Matter
Pages N1-XII
2. Herbert Gross
Pages 1-3
3. Herbert Gross
Pages 4-60
4. Herbert Gross
Pages 61-95
5. Herbert Gross
Pages 96-109
6. Herbert Gross
Pages 110-126
7. Herbert Gross
Pages 127-135
8. Herbert Gross
Pages 136-150
9. Herbert Gross
Pages 151-168
10. Herbert Gross
Pages 169-201
11. Herbert Gross
Pages 202-224
12. Herbert Gross
Pages 225-252
13. Herbert Gross
Pages 253-268
14. Herbert Gross
Pages 269-327
15. Herbert Gross
Pages 328-353
16. Herbert Gross
Pages 354-374
17. Herbert Gross
Pages 375-386
18. Herbert Gross
Pages 387-412
19. Back Matter
Pages 414-419

### Introduction

For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du­ ring this period, to wit, the results on denumerably infinite spaces (" ~O- forms") . Certain among the resul ts included here had of course been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I in­ clude results contained in the Ph.D.theses by my students w. Allenspach, L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ -dimensional 0 spaces ideally serves the purpose. First, these spaces show a large nurober of phenomena typical of infinite dimensional spaces. Second, most proofs can be done by recursion which resembles the familiar pro­ cedure by induction in the finite dimensional Situation. Third, the student acquires a good feeling for the linear algebra in infinite di­ mensions because it is impossible to camouflage problems by topological expedients (in dimension ~O it is easy to see, in a given case, wheth­ er topological language is appropriate or not) .

### Keywords

algebra proof recursion

#### Authors and affiliations

1. 1.Mathematisches InstitutUniversität ZürichZürichSwitzerland

### Bibliographic information

• Book Title Quadratic Forms in Infinite Dimensional Vector Spaces
• Authors Herbert Gross
• Series Title Progress in Mathematics
• Series Abbreviated Title Progress in Mathematics(Birkhäuser)
• DOI https://doi.org/10.1007/978-1-4757-1454-8
• Publisher Name Springer, Boston, MA
• eBook Packages
• Hardcover ISBN 978-0-306-39201-6
• Softcover ISBN 978-1-4757-1456-2
• eBook ISBN 978-1-4757-1454-8
• Series ISSN 0743-1643
• Series E-ISSN 2296-505X
• Edition Number 1
• Number of Pages XII, 419
• Number of Illustrations 2 b/w illustrations, 0 illustrations in colour
• Topics
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