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

### Authors:

- Artur Michalak

### Abstract

We say that a function f from [0, 1] to a Banach space X is increasing with respect to E ⊂ X* if x* o 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) lin{f([0, 1])} contains an order isomorphic copy of D(0, 1), (2) lin{f(Q)} contains an isomorphic copy of C([0, 1]), (3) lin{/([0, 1])}/lin{f(Q)} contains an isomorphic copy of c_{0}(Γ) for some uncountable set Γ, (4) if I is an isomorphic embedding of lin{f([0, 1])} into a Banach space Z, then no separable complemented subspace of Z contains I(lin{f(Q)}).

- Record ID
- UAMfd211d4082ec4f0da145b27617c0187f
- Author
- Journal series
- Studia Mathematica, ISSN 0039-3223
- Issue year
- 2003
- Vol
- 155
- Pages
- 171-182
- ASJC Classification
- DOI
- DOI:10.4064/sm155-2-6 opening in a new tab
- Language
- en English
- Score (nominal)
- 30
- Score source
- journalList
- Publication indicators
- = 5.000; : 2003 = 1.282; : 2006 = 0.515 (2) - 2007=0.673 (5)

- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAMfd211d4082ec4f0da145b27617c0187f/

* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perishopening in a new tab system.

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