Bases in the spaces C and L 1

S. J. Szarek

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980)

  • page 1-8

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Szarek, S. J.. "Bases in the spaces $C$ and $L^1$." Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz") (1979-1980): 1-8. <http://eudml.org/doc/109232>.

@article{Szarek1979-1980,
author = {Szarek, S. J.},
journal = {Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")},
keywords = {uniformly bounded orthonormal system; basis},
language = {eng},
pages = {1-8},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Bases in the spaces $C$ and $L^1$},
url = {http://eudml.org/doc/109232},
year = {1979-1980},
}

TY - JOUR
AU - Szarek, S. J.
TI - Bases in the spaces $C$ and $L^1$
JO - Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
PY - 1979-1980
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 8
LA - eng
KW - uniformly bounded orthonormal system; basis
UR - http://eudml.org/doc/109232
ER -

References

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  1. [1] S.V. Bočkariev: A Fourier series divergent on a set of positive measure for arbitrary uniformly bounded orthonormal system, Math. Sbor.98 (140) (1975), 436-449 (Russian). Zbl0315.42011MR390634
  2. [2] B.S. Kashin: Remarks on Lebesgue functions of orthonormal systems, Math. Sbor.106 (148) (1978), 380-385 (Russian). Zbl0417.42014MR619470
  3. [3] A.S. Krantzberg, On systems of convergence in C and bases in L, Math. Zam.26 (1979), 183-200 (Russian). Zbl0424.42016MR547430
  4. [4] S. Kwapień, S.J. Szarek: Estimation of Lebesgue functions of biorthogonal systems with application to bases, Studia Math.66 (2). Zbl0434.46015MR565158
  5. [5] A.M. Olevskiĭ, Fourier series with respect to general orthogonal systems, Springer-Verlag1975. Zbl0321.42010MR470599
  6. [6] A. Pełczyński: On a result of Olevskiĭ: a uniformly bounded orthonormal sequence is not a basis for C[0,1], Séminaire Maurey-Schwartz1973-74, Exposé No 21. Zbl0298.46024
  7. [7] I. Singer: Bases in Banach spaces I, Springer-Verlag1970. Zbl0198.16601MR298399
  8. [8] S.J. Szarek, Non existence of Besselian basis in C(S), J. Funct. Anal.36 (1980). Zbl0504.46017MR576645
  9. [9] S.J. Szarek: Bases and biorthogonal systems in the spaces C and L1, Arkiv f. Matematik17 (2) (1979), 255-271. Zbl0432.46016MR608319

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