Weak convergence for the covariance operators of a Hilbertian linear process

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Convolutional autoregressive models for functional time series (2016, unknown): “For the FAR model, Bosq (2000) only considered consistency, and Mas (2002) obtained a partial result on the weak convergence of the autoregressive operator.”
Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series (2013, background): “Work on this front was pioneered by Bosq [3, 4], who focussed on the estimation of spectral decompositions of autocovariance operators in the special case of stationary AR(1) functional process, work later extended to more general linear stationary functional processes (Mas [28, 29]; Bosq [6]).”
On properties of functional principal components analysis (2006, background): “Work of Dauxois et al. (1982), Bosq (1989), Besse (1992), Huang et al. (2002) and Mas (2002), for example, addresses the empirical basis function approximation and approximations of covariance operators, and so is directly related to our own.”
A survey of functional principal component analysis (2014, unknown): “( 2007 ) , Ferraty & Vieu ( 2006 ) , Mas ( 2002 ) , Mas ( 2008 ) , Bosq ( 2000 ) , among many others .”
Asymptotic normality of the principal components of functional time series (2013, background): “(They follow from more general results proved in [10,13], and used by many authors including [4,23].”