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Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces

Problems of existence of order copies of $$\ell ^\infty $$ ℓ ∞ and $$L_p(\nu )$$ L p ( ν ) in some non-Banach Köthe spaces

For a monotone Orlicz function $$\varPhi $$ taking only values 0 and $$\infty $$ , it is showed that in both cases, the s-homogeneous norm $$\Vert \cdot \Vert _{\varPhi ,s}$$ , if $$\varPhi $$ is s-convex $$(0<s\le 1)$$ and the Mazur–Orlicz F-norm $$\Vert \cdot \Vert _\varPhi $$ , if $$\varPhi …