A characterization of reflexive spaces by means of continuous approximate selections for metric projections

@article{Zhivkov1989ACO,
  title={A characterization of reflexive spaces by means of continuous approximate selections for metric projections},
  author={N. V. Zhivkov},
  journal={Journal of Approximation Theory},
  year={1989},
  volume={56},
  pages={59-71}
}
  • N. Zhivkov
  • Published 1989
  • Mathematics
  • Journal of Approximation Theory
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References

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Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection
Reflexivity and the sup of linear functionals
A relatively easy proof is given for the known theorem that a Banach space is reflexive if and only if each continuous linear functional attains its sup on the unit ball. This proof simplifies
Geometry of Banach Spaces: Selected Topics
Support functionals for closed bounded convex subsets of a Banach space.- Convexity and differentiability of norms.- Uniformly convex and uniformly smooth Banach spaces.- The classical renorming
Nonexistence of continuous selections of the metric projection for a class of weak Chebyshev spaces
The class 3 of all those n-dimensional weak Chebyshev subspaces of C[a, b] whose elements have no zero intervals is considered. It is shown that there does not exist any continuous selection of the
Characterization of Continuous Selections for the Metric Projection for Generalized Splines
In this paper we give a characterization of those generalized spline spaces which admit continuous selections for the metric projection. We denote by generalized splines those weak Chebyshev spaces
Nonexistence of Continuous Selections of the Metric Projection and weak Chebyshev Systems
We show that an n-dimensional subspace G of $C[a,b]$ which admits a continuous selection for the metric projection has to be weak Chebyshev. For $C[a,b]$ this solves one part of a problem posed by
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