Acta Mathematica

Subspaces and quotients of lp⊕l2 and Xp

W. B. Johnson and E. Odell

Full-text: Open access

Note

Part of the research for this paper was done while both authors were guests of the Institute for Advanced Studies of the Hebrew University of Jerusalem.

Note

Supported in part by NSF MCS76-06565 and MCS79-03042.

Note

Supported in part by NSF MCS78-01344.

Article information

Source
Acta Math., Volume 147 (1981), 117-147.

Dates
Received: 29 May 1980
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890133

Digital Object Identifier
doi:10.1007/BF02392872

Mathematical Reviews number (MathSciNet)
MR631092

Rights
1981 © Almqvist & Wiksell

Citation

Johnson, W. B.; Odell, E. Subspaces and quotients of l p ⊕l 2 and X p. Acta Math. 147 (1981), 117--147. doi:10.1007/BF02392872. https://projecteuclid.org/euclid.acta/1485890133


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References

  • Alspach, D., Enflo, P. & Odell, E., On the structure of separable Lp spaces (1< p<∞)Studia Math., 60 (1977), 79–90.
  • Bourgain, J., Rosenthal, H. P. & Schechtman, G., An ordinal Lp-index for Banach spaces, with application to complemented subspaces of Lp.
  • Casazza, P. G. & Lin, B.-L., Projections on Banach spaces with symmtric bases. Studia Math., 52 (1974), 189–193.
  • Edelstein, I. & Wojtaszczyk, P., On projections and unconditional bases in direct sums of Banach spaces. Studia Math., 56 (1976), 263–276.
  • Johnson, W. B., On quotients of Lp which are quotients of lpCompositio Math., 34 (1977), 69–89.
  • —, Operators into Lp which factor through lp. J. London Math. Soc., Ser. 2, 14 (1976), 333–339.
  • Johnson, W. B. & Jones, L., Every Lp operator is an L2 operator. Proc. Amer. Math. Soc. 72 (1978), 309–312.
  • Johnson, W. B., Maurey, B., Schechtman, G. & Tzafriri, L., Symmetric structures in Banach spaces. Mem. Amer. Math. Soc., 217 (1979).
  • Johnson, W. B. & Odell, E., Subspaces of Lp which embed into lp. Compositio Math., 28 (1974), 37–49.
  • Johnson, W. B., Rosenthal, H. P. & Zippin, M., On bases, finite dimensional decompositions and weaker structures in Banach spaces. Israel J. Math., 9 (1971), 488–506.
  • Johnson, W. B. & Zippin, M., On subspaces of quotients of (ΣGn)lp and (ΣGn)co. Israel J. Math., 13 (1972), 311–316.
  • — Subspaces and quotient spaces of (ΣGn)lp and (ΣGn)co. Israel J. Math., 17 (1974), 50–55.
  • Kadec, M. & Pelczynski, A., Bases, lacunary sequences and complemented subspaces in the spaces Lp. Studia Math., 21 (1962), 161–176.
  • Lindenstrauss, J. & Tzafriri, L., Classical Banach Spaces I, Sequence Spaces. Ergebnisse 92, Springer-Verlag (1977).
  • Lindenstrauss, J.Classical Banach Spaces II, Function Spaces. Ergebnisse 97, Springer-Verlag (1979).
  • Maurey, B., Théorèmes de factorisation pour les operateurs linéaires a valeurs dans les espaces Lp. Asterisque, #11, Soc. Math. de France. Paris (1974).