Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2003 | 155 | 2 | 171-182

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

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 $I(\overline{lin{f(Q)}})$.

171-182

wydano
2003

### Twórcy

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