Recent Advances in Operator-Related Function Theory

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On the connected component of compact composition operators on the Hardy space (2007, background): “By a variant of Fatou’s theorem, any Hardy function f has non-tangential limits on the boundary of the unit disc except on a set Lebesgue measure zero (see [8], for instance).”
The Dirichlet space: a survey (2010, background): “Much more can be said though, both on the kind of approach region and on the size of the exceptional set, see the papers [41], [44] and [56].”
Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity (2009, background): “Moreover, so is the Volterra integration operator, every 2 × 2 matrix, and every normal operator [10, 11].”