### Errata

While we hoped to have an error free book, it did not happen!

• Introduction
• page 7, line -3, Exercise 1.1.9: should be "j \geq 0" instead of "j>0"
• Analysis Background
• page 23, line -5: sentence should read "the Bergman space ... with \beta(s)^2=(s+1)^{-1}" instead of "\beta(s)"
• page 28, Exercise 2.1.13(b): sentence should read "the Bergman space ... choice \beta(s)^2=(s+1)^{-1}" instead of "\beta(s)"
• page 30, first display: ")" missing in first integral
• page 55: In Corollary 2.47, replace "{ z : r < |z| < 1 }" by "{ z : |\zeta - z| < 1-r }" in the statement and the proof (2 places)
(this makes the set \Gamma(\zeta,\alpha) \cap { z : |\zeta - z| < 1-r } convex)
• page 79: Corollary to Theorem 2.64 should be added Patch
• page 93, Exercise 2.4.1: "\phi(\sigma(z))" should be "\sigma(\phi(z))"
• page 93, Exercise 2.4.7: As Example 2.58 indicates, one of the hypotheses is omitted; the exercise should read " ...with \phi'(1)=1 and \phi is in the halfplane/translation case, then \phi maps ..."
• Norms
• page 127, Exercise 3.1.7: upper bound should be should be " \left( ( 1 + |\phi(0)| )/( 1 - |\phi(0)| ) \right)^{1/p} "
• page 127, Exercise 3.1.9: missing hypothesis: " | \lambda | = 1 "
• page 129, line 16: "apply of characterization" should be "apply the characterization"
• page 136, line -4 and line -7: "\|\C\|_e" should be "\|\C\|_e^2"
• page 139, line 7: "N_{\phi}(w)" should be "N_{\phi}(a)"
• page 166, line 2 of proof of Lemma 3.40: "\zeta=n=e_1" should be "\zeta=\eta=e_1"
• Small Spaces
• page 176, third display of Thm. 4.1: "boundary B_N" should be "boundary D"
• page 195, last line: "operator" should be "operators"
• Large Spaces
• page 202, Lemma 5.6: "|\phi(0)| = s" should be "|\phi(0)| \leq s"
• page 203, line -6: "|\phi(0)| = s ..." should be "|\phi(0)| \leq s < ..."
and "Y(r) = y(s,r)" should be "Y(r) \leq y(s,r)"
• page 207, Theorem 5.11: "A > 0" should be "A \geq 1"
• page 207, Theorem 5.11: "c independent of f" would be better said
"c depending only on r_0, t_0, and F"
• page 211, Notes, line -2: "no bounded, non-compact operators" should be
"no bounded, non-compact, composition operators"
• Special Results for Several Variables
• Spectral Properties
• page 276, line -2 of text: "[Cal62, page 331]" should be "[Cal52, page 331]" (which reference is added below)
• page 281: Lemma 7.25 should be revised to include some non-fixed points Patch
• page 283: Proof of Theorem 7.26 must be revised since Exercise 7.5.2 is incorrectly stated Patch
• page 288, Theorem 7.29: Hypothesis "z_0'=z_0" was omitted.
• page 288, Exercise 7.5.2: "\{ e^{i\theta} : |\phi_n(e^{i\theta})|=1 \}" should be
"\{ \phi_n(e^{i\theta}) : |\phi_n(e^{i\theta})|=1 \}". This necessitates changes on pages 79, 281, 283, and 296. Patch
• page 293, line -8: ")" should be deleted at the end of the sentence following the display
• page 296, line 7 (preceding third display): "\phi^{(K)}" should be "\phi_K"
• page 296, line -8: "\{ w : |w|=1 and |\phi_n(w)|=1 \}" should be
"\{ \phi_n(w) : |w|=1 and |\phi_n(w)|=1 \}". Patch
• page 293, line -8: ")" should be deleted at the end of the sentence
• page 301, line 22: "halfplane/translation" should be "plane/translation"
• page 304, line -11: "..spectrum and essential of.." should be "..spectrum and essential spectrum of.."
• Normality
• page 311, line 8: "H" should be "H^2(\beta,D)"
• page 312, Exercise 8.1.1(b) should read "Suppose C is a normal operator and ... "
• Miscellanea
• page 321, first display: norm should be replaced by "(...)" in third sum
• page 347, line -13: "interested the" should be "interested in the"
• Bibliography
• New entry:
[Cal52] L. Carleson, Sets of uniqueness for functions regular in the unit circle, Acta Math. 87(1952), 325-345.
• [Hu89]: date should be "1989".

 cowen@math.purdue.edu