An error was encountered while trying to add the item to the cart. Please try again.
Copy To Clipboard
Successfully Copied!
The Metric Theory of Tensor Products: Grothendieck’s Résumé Revisited

Joe Diestel Kent State University, Kent, OH
Jan H. Fourie North-West University, Potchefstroom, South Africa
Johan Swart University of Pretoria, Pretoria, South Africa
Available Formats:
Hardcover ISBN: 978-0-8218-4440-3
Product Code: MBK/52
List Price: $92.00 MAA Member Price:$82.80
AMS Member Price: $73.60 Electronic ISBN: 978-1-4704-2483-1 Product Code: MBK/52.E List Price:$86.00
MAA Member Price: $77.40 AMS Member Price:$68.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $138.00 MAA Member Price:$124.20
AMS Member Price: $110.40 Click above image for expanded view The Metric Theory of Tensor Products: Grothendieck’s Résumé Revisited Joe Diestel Kent State University, Kent, OH Jan H. Fourie North-West University, Potchefstroom, South Africa Johan Swart University of Pretoria, Pretoria, South Africa Available Formats:  Hardcover ISBN: 978-0-8218-4440-3 Product Code: MBK/52  List Price:$92.00 MAA Member Price: $82.80 AMS Member Price:$73.60
 Electronic ISBN: 978-1-4704-2483-1 Product Code: MBK/52.E
 List Price: $86.00 MAA Member Price:$77.40 AMS Member Price: $68.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$138.00 MAA Member Price: $124.20 AMS Member Price:$110.40
• Book Details

2008; 278 pp
MSC: Primary 46; 47;

Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical Banach spaces ($C(K)$'s, Hilbert spaces, and the spaces of integrable functions) fit naturally within the mosaic that Grothendieck constructed.

Graduate students and research mathematicians interested in abstract analysis, Banach space theory, functional analysis, and operator theory.

• Chapters
• Chapter 1. Basics on tensor norms
• Chapter 2. The role of $C(K)$-spaces and $L^1$-spaces
• Chapter 3. $\otimes$-norms related to Hilbert space
• Chapter 4. The fundamental theorem and its consequences
• Glossary of terms
• Appendix A. The problems of the Résumé
• Appendix B. The Blaschke selection principle and compact convex sets in finite dimensional Banach spaces
• Appendix C. A short introduction to Banach lattices
• Appendix D. Stonean spaces and injectivity
• Epilogue

• Reviews

• (The book) scores on several counts, not just as a serious scholarly contribution to functional analysis, but as a tribute to Grothendiecks incomparable gifts in the area of innovation and originality.

MAA Reviews
• The exposition is clear, well-motivated and reasonably self-contained.

Mathematical Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2008; 278 pp
MSC: Primary 46; 47;

Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical Banach spaces ($C(K)$'s, Hilbert spaces, and the spaces of integrable functions) fit naturally within the mosaic that Grothendieck constructed.

Graduate students and research mathematicians interested in abstract analysis, Banach space theory, functional analysis, and operator theory.

• Chapters
• Chapter 1. Basics on tensor norms
• Chapter 2. The role of $C(K)$-spaces and $L^1$-spaces
• Chapter 3. $\otimes$-norms related to Hilbert space
• Chapter 4. The fundamental theorem and its consequences
• Glossary of terms
• Appendix A. The problems of the Résumé
• Appendix B. The Blaschke selection principle and compact convex sets in finite dimensional Banach spaces
• Appendix C. A short introduction to Banach lattices
• Appendix D. Stonean spaces and injectivity
• Epilogue
• (The book) scores on several counts, not just as a serious scholarly contribution to functional analysis, but as a tribute to Grothendiecks incomparable gifts in the area of innovation and originality.

MAA Reviews
• The exposition is clear, well-motivated and reasonably self-contained.

Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.