Continuity of coordinate functionals of filter bases in Banach spaces

We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long underlying is analytic. This removes large-cardinal hypothesis from result established by two last-named authors (Kania and Swaczyna, 2021 [9]) at expense of reducing generality projective to In particular, we obtain a ZFC solution Kadets' problem continuity respect statistical convergence. Even though automatic beyond class remains mystery, basis an arbitrary has also