The Backward Shift on the Hardy Space

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Symbols of truncated Toeplitz operators (2010, background): “It is well known that, for 1 6 p 6 ∞, any closed subspace of Hp invariant with respect to the backward shift (S∗f)(z) = f(z)−f(0) z is of the formK p θ for some inner function θ (see [22, Chapter II] or [14]).”
Complex Symmetric Operators and Applications II (2005, background): “It is well known (see [10] for example) that the proper, nontrivial invariant subspaces for the backward shift operator are precisely the subspaces”
Backward shift invariant subspaces in the bidisc II (2003, background): “invariant subspaces of the unit circle i; see [ 3 ] and [12].”
Conjugation and Clark Operators (2006, background): “Indeed, Mz has no eigenvalues while M z (the backward shift) has many [ 8 , 30].”
Recent Progress on Truncated Toeplitz Operators (2011, methodology): “We refer the reader to the references [5,27,39,83] for further infor1 Equivalently, G(1/z) ∈ Hp 0 .”
Admissible Majorants for Model Subspaces of H 2, Part I: Slow Winding of the Generating Inner Function (2003, methodology): “Their properties and numerous connections with various topics in analysis can be found, e.g., in the work of Douglas, Shapiro, Shields [11], Cohn [9], Dyakonov [13], Volberg [32], Treil [33], Nikolski [29], Ahern, Clark [1], Alexandrov [2], and in the monograph of Cima, Ross [8].”