Linear selections for the metric projection

@article{Deutsch1982LinearSF,
  title={Linear selections for the metric projection},
  author={Frank Deutsch},
  journal={Journal of Functional Analysis},
  year={1982},
  volume={49},
  pages={269-292}
}
  • F. Deutsch
  • Published 1 December 1982
  • Mathematics
  • Journal of Functional Analysis
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33 Citations
Highly Influential Citations
2
Background Citations
8
Methods Citations
1
Results Citations
2

33 Citations

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…
Remarks on linear selections for the metric projection
The linear selections of metric projections in the L p spaces
Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces
Nonexpansive selections of metric projections in spaces of continuous functions
NORM-ONE PROJECTIONS IN BANACH SPACES
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…
Norm-one projections onto subspaces of finite codimension in ℓ1 andc0
We study 1-complemented subspaces of the sequence spaces ℓ1 andc0. In ℓ1, 1-complemented subspaces of codimensionn are those which can be obtained as intersection ofn 1-complemented hyperplanes.…
The existence of linear selection and the quotient lifting property
Lifting properties for Banach spaces are studied. An alternate version of the lifting property due to Lindenstrass and Tzafriri is proposed and a characterization, up to isomorphism, is given. The…
The contraction linear metric projections inLp spaces
In this paper, we study the contraction linearity for metric projection in Lp spaces. A geometrical property of a subspace Y of Lp is given on which Py is a contraction projection.
Tietze extensions and continuous selections for metric projections
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References

SHOWING 1-10 OF 32 REFERENCES
Pointwise-Lipschitz-continuous selections for the metric projection
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…
Chebyshev subspaces of L1 with linear metric projection
Continuous selections for the metric projection and alternation
Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
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…
On continuous selections for metric projections in spaces of continuous functions
Some complemented function spaces in C(X)
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…
On the complemented subspaces problem
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…
INVARIANT SUBSPACES OF COMPLETELY CONTINOUS OPERATIONS
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…
CONTINUOUS SELECTIONS FOR METRIC PROJECTIONS
A remark on the lower semi-continuity of the set-valued metric projection
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