Prerequisites for Bourbaki spectral theory (French)

Question

I am considering reading Bourbaki's text Théories spectrales (Springer, French, 2nd Ed.) and was wondering what the prerequisites are. Currently I am familiar with their texts on the Theory of Sets, General Topology (Chaps 1-4 and 5-10), Topological Vector Spaces, Algebra I (Chaps 1-3), and Integration (Chaps 1-6 and 7-9). Do I also need familiarity with their text on Commutative Algebra?

Thanks.

Answer 1

I have the book and have seen no uses/references of/to commutative algebra. The only books which are in substantial use are his books on topology (Topologie Générale), topological vector spaces (Espaces Vectoriels Topologiques), and integration (Intégration). Occasionally (maybe once or twice throughout the book) are there references to the recent text on algebraic topology (Topologie Algébrique) and to his first text on algebra; the references to these books, however, only seem to appear in the exercise. There are a few (maybe 3 at most) references to his (reference) book on differential geometry, and a few references to his text on functions of a real variable.

In summary, the prerequisites are

  (i) General Topology I-IV and V-X,

  (ii) Topological Vector Spaces I-V,

  (iii) Integration I-VI and VII-IX, and

  (iv) (Elementary) Differential Geometry + Complex Analysis,

to read and understand the book, and

  (v) Algebra

to complete some of the more applied exercises.