Double Operator Integrals in a Hilbert Space

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On regularization algorithms in learning theory (2007, background): “The fact that an operator valued function ϑ is Lipschitz continuous if a real function ϑ is Lipschitz continuous follows from Theorem 8.1 in Birman and Solomyak (2003).”
Smooth Fourier multipliers on group von Neumann algebras (2010, methodology): “f(x) −f(y) x−y dµ(x)adν(y) have been intensively studied in the literature, following Birman/Solomyak we ﬁnd results from de Pagter/Sukochev and the impressive recent work of Peller, see for instance [2, 3, 8, 23, 24] and the references therein. Of course, we may understand this theory as a continuo”
Learning Sets with Separating Kernels (2012, background): “Assumption 2.c) and Theorem 8.1 in [8] (see also Lemma 5 in A.2 for a simple unpublished proof due to A. Maurer) imply that Inequality (26) then follows.”
Multiple operator integrals and higher operator derivatives (2005, background): “Later Birman and Solomyak developed their beautiful theory of double operator integrals in [BS1], [BS2], and [BS3] (see also [ BS4 ]); we discuss briefly this theory in §3.”