Title: Density of Analytic Polynomials in Abstract Hardy Spaces,
Abstract: Let $X$ be a separable Banach function space on the unit circle $\mathbb{T}$
and $H[X]$ be the abstract Hardy space built upon $X$. We show that the set of
analytic polynomials is dense in $H[X]$ if the Hardy-Littlewood maximal
operator is bounded on the associate space $X'$. This result is specified to
the case of variable Lebesgue spaces.