On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity

• Autorzy: Artur Michalak
• 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. We show that if f: [0,1] → X is an increasing function with respect to a norming subset E of X* with uncountably many points of discontinuity and Q is a countable dense subset of [0,1], then (1) $\overline{lin{f([0,1])}}$ contains an order isomorphic copy of D(0,1), (2) $\overline{lin{f(Q)}}$ contains an isomorphic copy of C([0,1]), (3) $\overline{lin{f([0,1])}}/\overline{lin{f(Q)}}$ contains an isomorphic copy of c₀(Γ) for some uncountable set Γ, (4) if I is an isomorphic embedding of $\overline{lin{f([0,1])}}$ into a Banach space Z, then no separable complemented subspace of Z contains $I(\overline{lin{f(Q)}})$.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 2
• Strony: 171-182

Daty

wydano

2003

Twórcy

autor

Artur Michalak

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

Identyfikatory

DOI

10.4064/sm155-2-6