Topological and algebraic genericity and spaceability for an extended chain of sequence spaces

Given a pair of topological vector spaces X,Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X,\; Y$$\end{document} where X is a proper linear subspace of Y it is examined whether Y\X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y\setminus X$$\end{document} is residual in Y (topological genericity), whether Y\X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y\setminus X$$\end{document} contains a dense linear subspace of Y except 0 (algebraic genericity) and whether Y\X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y\setminus X$$\end{document} contains a closed infinite dimensional subspace of Y except 0 (spaceability). In the present paper the spaces X and Y are either sequence spaces or spaces of analytic functions on the unit disc regarded as sequence spaces via the identification of a function with the sequence of its Taylor coefficients. For the spaces under consideration we give an affirmative answer to each of these questions providing general proofs which extend previous results.