The Metric Theory of Tensor Products by Joe Diestel (PDF)

Description

Grothendieck’s Resume 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.

User’s Reviews

Editorial Reviews: Review (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 ReviewsThe exposition is clear, well-motivated and reasonably self-contained. —- Mathematical Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This particular book does introduce the reader to the, partially wicked, world of tensor products and tensor norms. While the notation is a little unusual from time to time it is written very well, and the style of writing deserves the attribute “relaxed”. Don’t be fooled by the relaxed kind of writing! It is a quite advanced text being in need of your whole focussing on the subject. While I would have given it 5 stars I needed to subtract one due to a typo in the theorem on page 4. The proof following the theorem is actually wrong in a lot of respect, which the reader could find out by itself. To some extend the theorem just tells you, that the tensor product is unique up to isomorphism. I really hope this error to be corrected in another edition. Since I haven’t read the book completely by now, there haven’t been any other typos I detected thus far. Anyway….This book is definitely worth reading, if you are interested in the particular field of tensor products.

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