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On subsequences of the Haar system inL p [0, 1], (1<p<∞)

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Abstract

We show that ifX is the closed linear span inL p [0,1] of a subsequence of the Haar system, thenX is isomorphic either tol p or toL p [0,1], [1<p<∞]. We give criteria to determine which of these cases holds; for a given subsequence, this is independent ofp.

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References

  1. T. Ando,Banachverbände und positive Projektionen, Math. Z.109 (1696), 121–130.

    Article  MathSciNet  Google Scholar 

  2. C. Bessaga and A. Pełcyznski,On bases and unconditional convergence of series in Banach spaces, Studia Math.17 (1958), 151–164.

    MATH  MathSciNet  Google Scholar 

  3. N. Dunford and J. T. Schwartz,Linear Operators I, New York, 1958.

  4. W. B. Johnson, H. P. Rosenthal and M. Zippin,On bases, finite dimensional decompositions and weaker structures in Banach spaces, Israel J. Math.9 (1971), 488–506.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Lindenstrauss and A. Pełczyński,Absolutely summing operators in ℒ p-spaces and their applications, Studia Math.29 (1968), 275–326.

    MATH  MathSciNet  Google Scholar 

  6. J. Lindenstrauss and A. Pełczyński,Contributions to the theory of the classical Banach spaces, J. Functional Analysis8 (1971), 225–249.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Lindenstrauss and H. P. Rosenthal,The ℒ p-spaces, Israel J. Math.7 (1969), 325–349.

    Article  MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  9. H. P. Rosenthal,On the subspaces of L p (p>2) spanned by sequences of independent random variables, Israel J. Math.,8 (1970), 237–303.

    Article  Google Scholar 

  10. I. Singer,Bases in Banach spaces I, Springer-Verlag, New York, 1970.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Yale University, New Haven, Connecticut, U. S. A.

    J. L. B. Gamlen & R. J. Gaudet

  2. University of Alberta, Edmonton, Alberta, Canada

    J. L. B. Gamlen & R. J. Gaudet

  3. University of Saskatchewan, Saskatoon, Saskatchewan, Canada

    J. L. B. Gamlen & R. J. Gaudet

Authors
  1. J. L. B. Gamlen
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  2. R. J. Gaudet
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Additional information

This is part of the second author's Ph.D. dissertation, written at the University of Alberta under the supervision of J. L. B. Galmen. The first author's research was partially supported by NRC A7552.

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Gamlen, J.L.B., Gaudet, R.J. On subsequences of the Haar system inL p [0, 1], (1<p<∞). Israel J. Math. 15, 404–413 (1973). https://doi.org/10.1007/BF02757079

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  • DOI: https://doi.org/10.1007/BF02757079

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