Orthogonal uniform convexity in Köthe spaces and Orlicz spaces

• Autorzy: Kolwicz P.
• Języki publikacji: EN

Abstrakty

EN

We study a geometric property in Köthe spaces which is called orthogonal uniform convexity (UC┴). It was introduced in [19]. We prove that the class of Köthe spaces with property (UC┴) is a proper subset of the class of uniformly monotone and P-convex Köthe spaces. Next we consider connections between (UC┴) and property (β) of Rolewicz. We shown that the implication (UC┴) → (β) is true in any Köthe sequence space. Moreover, we find criteria for Orlicz function (sequence) spaces to be orthogonally uniformly convex. As a corollary we get that there holds (UC) → (UC┴) → (β) in any Köthe sequence space and the converse of any of these implications is not true. Furthermore, the implications (UC) → (β) → (UC┴) hold in any Köthe function space and the second one cannot be reversed.

Słowa kluczowe

EN

Köthe space; Orlicz space; P-convexity; property Beta; uniform convexity; uniform monotonicity

PL

monotoniczność jednostajna; p-wypukłość; przestrzeń Köthe'a; przestrzeń Orlicza; wypukłość jednostajna

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 4
• Strony: 395--411
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Kolwicz P.

• Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland,

Bibliografia

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