On Some Properties of Separately Increasing Functions from [0,1ⁿ into a Banach Space

• Autorzy: Michalak A.

Identyfikatory

DOI

10.4064/ba62-1-7

• Języki publikacji: EN

Abstrakty

EN

We say that a function f from [0,1] to a Banach space X is increasing with respect to E⊂X* if x∗∘f is increasing for every x*∈E. A function f:[0,1]^m→X is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c0 or such that X* is separable, then for every separately increasing function f:[0,1]^m→X with respect to any norming subset there exists a separately increasing function g:[0,1]^m→R such that the sets of points of discontinuity of f and g coincide.

Słowa kluczowe

EN

increasing vector functions; Banach space

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no 1
• Strony: 61--76
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Michalak A.

• Faculty of Mathematics and Computer Science Adam Mickiewicz University Umultowska 87 61-614 Poznań, Poland

Bibliografia

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