The conditional central limit theorem in Hilbert spaces

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On the Weak Invariance Principle for Non-Adapted Sequences under Projective Criteria (2007, unknown): “Remark 11 In Theorem 5 of Dedecker and Merlevède [7], a similar result was given, but for causal linear processes and causal innovations only, that is X0 = ∑ i≥0 aiε−i , ε0 is regular and M0-measurable, and ∑ i≥0 ‖P0(εi)‖2 <∞.”
Komlós–Major–Tusnády approximation under dependence (2014, background): “(2.2) Results of the above type have been known for several decades; see Hannan (1979), Woodroofe (1992), Volný (1993) and Dedecker and Merlevède (2003) among others.”
STRONG INVARIANCE PRINCIPLES FOR DEPENDENT RANDOM VARIABLES (2007, background): “For recent contributions see Merlevède and Peligrad [38], Wu and Woodroofe [67] and Peligrad and Utev [40], where the central limit theory and weak convergence problems are considered.”
Weak invariance principles for sums of dependent random functions (2013, methodology): “In the real valued case, the martingale approach to weak dependence was developed by Gordin [16], Philipp and Stout [25] and Eberlein [14], and by using such techniques [23,9] obtained central limit theorems for a large class of dependent variables in Hilbert spaces.”