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Projections onto L 1 subspaces of L1(μ)

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Banach Spaces, Harmonic Analysis, and Probability Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 995))

Abstract

If X is a L1, 1+ɛ subspace of L1(μ) and ɛ > 0 is sufficiently small, then X is complemented.

Supported in part by NSF MCS-802510.

Supported in part by NSF MCS-7903042.

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References

  1. L. Dor, On Projections in L1, Annals of Math. 102 (1975), 463–474.

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  2. L. Dor, On Embedding of Lp-spaces in Lp-spaces, Dissertation, The Ohio State University, 1975.

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  3. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Springer-Verlag, Berlin, 1977.

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  5. A. Pełczyński, Projections in certain Banach Spaces, Studia Math 19 (1960), 209–228.

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  6. M. Zippin, L 1 subspaces of ℓ1, Israel J. Math 22 (1975), 110–117.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Oklahoma State University, 74078, Stillwater, OK

    Dale E. Alspach

  2. Department of Mathematics, University of Connecticut, 06268, Storrs, CT

    Dale E. Alspach

  3. Department of Mathematics, Ohio State University, 43210, Columbus, OH

    William B. Johnson

  4. Department of Mathematics, Texas A&M University, 77843, College Station, TX

    William B. Johnson

Authors
  1. Dale E. Alspach
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  2. William B. Johnson
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Editor information

Ron C. Blei Stuart J. Sidney

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© 1983 Springer-Verlag

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Alspach, D.E., Johnson, W.B. (1983). Projections onto L 1 subspaces of L1(μ). In: Blei, R.C., Sidney, S.J. (eds) Banach Spaces, Harmonic Analysis, and Probability Theory. Lecture Notes in Mathematics, vol 995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061884

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  • DOI: https://doi.org/10.1007/BFb0061884

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12314-9

  • Online ISBN: 978-3-540-40036-3

  • eBook Packages: Springer Book Archive

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