Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A special basis for $ C([0,\,1])$


Author: H. E. Warren
Journal: Proc. Amer. Math. Soc. 27 (1971), 495-499
MSC: Primary 46.25
DOI: https://doi.org/10.1090/S0002-9939-1971-0270130-8
MathSciNet review: 0270130
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper constructs a basis for $ C([0,1])$ which converges weakly to zero whose elements are nevertheless norm bounded away from zero.


References [Enhancements On Off] (What's this?)

  • [1] C. Foiaş and I. Singer, On bases in $ C([0,1])$ and $ {L^1}([0,1])$, Rev. Roumaine Math. Pures Appl. 10 (1965), 931-960. MR 34 #6509. MR 0206691 (34:6509)
  • [2] J. R. Holub, Some problems concerning bases in Banach spaces, Proc. Amer. Math. Soc. 23 (1969), 521-525. MR 0250029 (40:3270)
  • [3] J. T. Marti, Introduction to the theory of bases, Springer Tracts in Natural Philosophy, vol. 18, Springer-Verlag, New York, 1969. MR 0438075 (55:10994)
  • [4] I. Singer, Basic sequences and reflexivity of Banach spaces, Studia Math. 21 (1961/62), 351-369. MR 26 #4155. MR 0146635 (26:4155)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.25

Retrieve articles in all journals with MSC: 46.25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0270130-8
Keywords: Basis, Schauder basis, weakly closed basis, $ C([0,1])$
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society