We compute the complexity of the classes of operators $${\mathfrak {G}}_{\xi , \zeta }\cap {\mathcal {L}}$$ G ξ , ζ ∩ L and $${\mathfrak {M}}_{\xi , \zeta }\cap {\mathcal {L}}$$ M ξ , ζ ∩ L in the coding of operators between separable Banach spaces. We also prove the non-existence of universal factoring operators for both $$\complement {\mathfrak {G}}_{\xi , \zeta }$$ ∁ G ξ , ζ and $$\complement {\mathfrak {M}}_{\xi , \zeta }$$ ∁ M ξ , ζ . The latter result is an ordinal extension of a result of Johnson and Girardi.

中文翻译：

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一些有序的确定类运算符的复杂性

我们计算算子 $${\mathfrak {G}}_{\xi , \zeta }\cap {\mathcal {L}}$$ G ξ , ζ ∩ L 和 $${\mathfrak { M}}_{\xi , \zeta }\cap {\mathcal {L}}$$ M ξ , ζ ∩ L 在可分离 Banach 空间之间的算子编码中。我们还证明了 $$\complement {\mathfrak {G}}_{\xi , \zeta }$$ ∁ G ξ , ζ 和 $$\complement {\mathfrak {M} }_{\xi , \zeta }$$ ∁ M ξ , ζ . 后一个结果是 Johnson 和 Girardi 的结果的序数扩展。