Bases in the spaces C and L 1

S. J. Szarek

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

  • page 1-8

How to cite


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

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 = {},
year = {1979-1980},

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 -
ER -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.