Linear selections for the metric projection

  title={Linear selections for the metric projection},
  author={Frank Deutsch},
  journal={Journal of Functional Analysis},
  • F. Deutsch
  • Published 1 December 1982
  • Mathematics
  • Journal of Functional Analysis
Selections For Metric Projections
A review is given of conditions which characterise when the metric projection onto a proximinal subspace of a normed linear space has a selection which is continuous, (pointwise) Lipschitz
This is a survey of results about norm-one projections and 1- complemented subspaces in K¨othe function spaces and Banach sequence spaces. The historical development of the theory is presented from
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The existence of linear selection and the quotient lifting property
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In a series of papers the last two authors have obtained a complete characterization of those finite-dimensional subspaces G of C[a,b] for which there exists a continuous selection for the metric
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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
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et X and Z be compact Hausdorff spaces, and let P be a linear subspace of C(X) which is isometrically isomorphic to C(Z). In this paper conditions, some necessary and some sufficient, are presented
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A Banach space is isomorphic to a Hilbert space provided every closed subspace is complemented. A conditionally σ-complete Banach lattice is isomorphic to anLp-space (1≤p<∞) or toc0(Γ) if every
Abstract : A proof is presented of the theorem that if B is a Banach space and if T is a completely continuous operator in B, there then exist proper invariant subspaces of T. The proof assumes