Let $u$ be an inner function and denote by $H^2$ the Hardy space on the open unit disc D. A model space $K_u$ associated to $u$ is a Hilbert space of the form $K_u=(uH^2)^⊥$ where ⊥ denotes the orthogonal complement in $H^2$. Does FLT still true in $K_u$ when u is an infinite Blaschke product ?
NB: It was shown that FLT is true for $K_u$ when u is a finite Blaschke product (cf. Stephan Ramon Garcia, Javad Mashreghi, William T. Ross - Introduction to Model Spaces and their Operators-Cambridge University Press (2016), p. 125).
What about the general case when $u$ is an arbitrary inner function ?