Quadratic Forms in Infinite Dimensional Vector Spaces: 1 (Progress in Mathematics, 1) - Tapa blanda

Gross, H.

 
9780817611118: Quadratic Forms in Infinite Dimensional Vector Spaces: 1 (Progress in Mathematics, 1)
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ISBN 10: 0817611118 ISBN 13: 9780817611118
Editorial: Birkhäuser, 1979

Sinopsis

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 (" NO-forms"’). Certain among the results 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 N-dimensional O spaces ideally serves the purpose. First, these spaces show a large number 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 NO it is easy to see, in a given case, wheth­ er topological language is appropriate or not).

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Reseña del editor

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 (" NO-forms'''). Certain among the results 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 N-dimensional O spaces ideally serves the purpose. First, these spaces show a large number 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 NO it is easy to see, in a given case, wheth­ er topological language is appropriate or not).

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Editorial
Birkhäuser
Año de publicación
1979
Idioma
Inglés
ISBN 10 
0817611118
ISBN 13 
9780817611118
Encuadernación
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Número de páginas
436
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

9781475714562: Quadratic Forms in Infinite Dimensional Vector Spaces: 1 (Progress in Mathematics, 1)

Edición Destacada

ISBN 10:  1475714564 ISBN 13:  9781475714562
Editorial: Springer, 2013
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