The complexity of some ordinal determined classes of operators

We compute the complexity of the classes of operators Gξ,ζ∩L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {G}}_{\xi , \zeta }\cap {\mathcal {L}}$$\end{document} and Mξ,ζ∩L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak {M}}_{\xi , \zeta }\cap {\mathcal {L}}$$\end{document} in the coding of operators between separable Banach spaces. We also prove the non-existence of universal factoring operators for both ∁Gξ,ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\complement {\mathfrak {G}}_{\xi , \zeta }$$\end{document} and ∁Mξ,ζ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\complement {\mathfrak {M}}_{\xi , \zeta }$$\end{document}. The latter result is an ordinal extension of a result of Johnson and Girardi.