Periodica Mathematica Hungarica

, Volume 22, Issue 3, pp 161–174 | Cite as

Norm-one projections onto subspaces of finite codimension in ℓ1 andc0

  • M. Baronti
  • P. Papini


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. Inc0, we prove a characterization of 1-complemented subspaces of finite codimension in terms of intersection of hyperplanes.

Mathematics subject classification numbers, 1980/85

Primary 46B99 Secondary 41A65 

Key words and phrases

Sequence spaces projections 


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  1. [1]
    M.Baronti, P. L.Papini, Norm-one projections onto subspaces ofl p,Annali Mat. Pura Appl. (4)152 (1988), 53–61.MR 89k:46031Google Scholar
  2. [2]
    H.Berens, G. G.Lorentz, Sequences of contractions onL 1 spaces,J. Funct. Anal. 15 (1974), 155–165MR 50:865Google Scholar
  3. [3]
    S. J.Bernau, Theorems of Korovkin type forL p-spaces,Pacific J. Math. 53 (1974), 11–19MR 52:14786Google Scholar
  4. [4]
    J.Blatter, E. W.Cheney, Minimal projections on hyperplanes in sequence spaces,Annali Mat. Pura Appl. (4)101 (1974), 215–227MR 50:10644Google Scholar
  5. [5]
    B.Calvert, The range of a contractive projection,Math. Chronicle 6 (1977), 68–71MR 57:10413Google Scholar
  6. [6]
    B.Calvert, S.Fitzpatrick, Characterizingl p andc 0 by projections onto hyperplanes,Boll. Un. Mat. Ital. (6)5-C (1986), 405–410MR 88f:46048Google Scholar
  7. [7]
    S.Campbell, G.Faulkner, R.Sine, Isometries, projections and Wold decompositions,Research Notes in Math. (Operator Theory and Functional Analysis) (ed. by I.Erdélyi)38 85–114, Pitman, London, (1979),MR 81k:47041Google Scholar
  8. [8]
    E. W. Cheney, C. Franchetti, Minimal projections of finite rank in sequence spaces,Fourier Analysis and Approximation Theory, Coll. Math. Soc. János Bolyai n.19 ( G. Alexits-P. Turán), Budapest, (1976), 241–253.MR 84b:46010Google Scholar
  9. [9]
    E. W.Cheney, K. H.Pryce, Minimal projections,Approximation Theory (ed. by A.Talbot), 261–289; Academic Press, New York (1970),MR 42:751Google Scholar
  10. [10]
    F.Deutsch, Linear selections for the metric projections,J. Funct. Anal. 49 (1982), 269–292.MR 84a:41029Google Scholar
  11. [11]
    F. Deutsch, When does the metric projection admit a linear selection?,Proc. 2nd Edmonton Conf. on Approx. Th., 135–141. (CMS Conf. Proc., AMS, Providence, R. I. (1983)).MR 85b:41038Google Scholar
  12. [12]
    F.Deutsch, A survey of metric selections,Fixed points and nonexpansive mappings (ed. by R.C.Sine) 49–71; Contemporary Mathematics Vol. 18, AMS, Providence, R. I. (1983).MR 85b:41037Google Scholar
  13. [13]
    F.Deutsch, V.Indumathi, K.Schnatz, Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings,J. Approx. Th. 33 (1988), 266–294MR 89g:54042Google Scholar
  14. [14]
    Y.Friedman, B.Russo, Contractive projections onC 0 (K),Trans. Amer. Math. Soc. 273 (1982), 57–73.MR 83i:46062Google Scholar
  15. [15]
    C.-H. Kan, Nonextremeness of non-identical contractive projections onL p,(preprint.) Google Scholar
  16. [16]
    H. E.Lacey,The isometric theory of classical Banach spaces, Springer-Verlag, Berlin (1974),MR 58:12308Google Scholar
  17. [17]
    P.-K.Lin, Remarks on linear selections for the metric projection,J. Approx. Th. 43 (1985), 64–74MR 86f:41008Google Scholar
  18. [18]
    R.Sine, Rigidity properties of nonexpansive mappings,Nonlin. Anal. 11 (1987), 777–794.MR 88i:47031Google Scholar
  19. [19]
    R. S.Strichartz,L P contractive projections and the heat semigroup for differential forms,J. Funct. Anal. 65 (1986), 348–357.MR 87e:58192Google Scholar
  20. [20]
    U.Westphal, Cosuns inl P (n), 1≤p<∞,J. Approx. Th. 54 (1988), 287–305.MR 89m:41207Google Scholar
  21. [21]
    D. E.Wulbert, Contractive Korovkin approximations,J. Funct. Anal. 19 (1975), 205–215.MR 52:6385Google Scholar
  22. [22]
    M.Zippin, The range of a projection of small norm inl 1n,Israel J. Math. 39 (1981), 349–358.MR 83h:46031Google Scholar

Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • M. Baronti
    • 1
  • P. Papini
    • 2
  1. 1.Dipartimento di MatematicaANCONAITALY
  2. 2.Dipartimento di MatematicaBOLOGNAITALY

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