Barry Simon (1) (1946–)

Minor Notes

[SEE UPDATE BELOW]

Obviously, this and the other 4 volumes in the series are fated to become classic texts for higher-level analysis. Some few of you may be curious about the rate of errata for 3000+ pages of newly-printed math. Here's what I've found after finishing the first chapter:

1) In the Preface, Niels Bohr is called "Neils".
2) The definition of a well-ordered set on Page 10 neglects to mention that it is only *nonempty* subsets that require a smallest element.
3) We are told specifically that Z_+ and C_+ exclude 0, but we don't seem to be told about R_+. If it also excludes 0, then the statement on Pages 10 and 11 that every (nonempty?) subset of R_+ has an infimum would seem to fail.
4) On Page 16, Aleph_{n+1} is mischaracterized as being equal to 2^{Aleph_n} (as if the GCH were assumed true).
5) In formula (1.7.3) on Page 18, x_ell should be y_ell.
6) In the proof of Proposition 1.7.2 on Page 20, X and W are mixed up with x and w.
7) In the second paragraph of the proof of Proposition 1.7.7 on Page 23, projection operators seem to lose their subscripts.
8) In the sketch of the proof of Theorem 1.8.4 on Page 32, "sup" should be "supp".
9) "Bounded sequence on increasing reals" (p. 16), "is group homomorphism" (p. 18), and "finite linear combination are dense" (p. 18) were probably not meant to read exactly that way.

Some few of you might also wonder about the physical construction of the books in the series. They are similar to recent books in the GSM series: non-glossy, pure-white paper with sewn bindings.

UPDATE 1: I've only made incremental progress in Simon's series in the last few years, but every time I've dipped into it to see his treatment of a subject I've been blown away at how good it is, in the sense of clarity and completeness (even if there may be an occasional typo). He makes difficult things look simple . . . by making them simple indeed! My dumb list of typos above is far from a good summary of the quality of this series.

UPDATE 2: The physical quality of AMS books has gone downhill in the last couple of years: Not enough ink/toner, and you can't count on getting a sewn binding. Get a copy of Simon's series that is made the old way.… (altro)