Notes and corrections for the cartesian decompositions book

• Lemma 2.19, Corollary 2.21 and Theorem 3.2
• Lemma 2.37
• Lemma 3.1
• Page 105

Other small errors and typos (reported by Lei Chen):

• Proof of Theorem 3.12 (i), page 55, line -3 of the proof of (i): $N$ should be $N\chi$.
• Proof of Corollary 3.13, page 57, line 1: $K \vartheta$ should be $K\chi$.
• Claim 2 in Proposition 3.20, page 63:
  • $\Omega$ is the set being acted on.
  • In line 1 of the proof of this claim, $\gamma$ and $\delta$ are both contained in $\Sigma_1$ and both contained in $\Sigma_2$.
• Page 83 line -2: In the display, the last entry on the right-hand side should be $c_k(t_1\varphi_k)$.