Pacific Journal of Mathematics

Unconditional and shrinking bases in locally convex spaces.

L. J. Weill

Article information

Source
Pacific J. Math., Volume 29, Number 2 (1969), 467-483.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102982984

Mathematical Reviews number (MathSciNet)
MR0246083

Zentralblatt MATH identifier
0176.10802

Subjects
Primary: 46.01

Citation

Weill, L. J. Unconditional and shrinking bases in locally convex spaces. Pacific J. Math. 29 (1969), no. 2, 467--483. https://projecteuclid.org/euclid.pjm/1102982984


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References

  • [1] C. Bessaga and A. Pelczynski, A generalization of results of R. C. James con- cerning absolute bases in Banach spaces, Studia Math. 17 (1958), 165-174.
  • [2] M. M. Day, Normed linear spaces, rev. ed., Academic Press, Inc., New York, 1962.
  • [3] J. Dieudonne, On biorthogonal systems, Michigan Math. J. 2 (1954), 7-20.
  • [4] J. Dieudonne and L. Schwartz, La dualite dans les espaces (F) et (LF), Ann. Inst. Fourier Grenoble 1 (1949), 61-101.
  • [5] E. L. Dubinsky and J. R. Retherford, Schauder bases and Koike sequence spaces, Trans. Amer. Math. Soc. 130 (1968), 265-280.
  • [6] A. Grothendieck, Sur les applications lineaires faiblement compactes d'espace du type C(K), Canad. J. Math 5 (1953), 169-173.
  • [7] L. A. Gurevic, On unconditional bases, Uspehi Matem. Nauk (N. S.) 8 (1953), 153-156.
  • [8] R. C. James, Bases and reflexivity of Banach spaces, Ann. of Math. (2) 52 (1950), 518-527.
  • [9] S. Karlin, Bases in Banach spaces, Duke Math. J. 15 (1948), 971-985.
  • [10] J. L. Kelly, I. Namioka, et al., Linear topological spaces, D. Van Nostrand Co., Inc., Princeton, 1963.
  • [11] C. W. McArthur, A convergence criterion with applications to series in locally convex spaces, Duke Math J. 34 (1967), 193-200.
  • [12] C. W. McArthur, On a theorem of Orlicz and Pettis, Pacific J. Math. 22 (1967), 297-302.
  • [13] J. R. Retherford, Bases, basic sequences and reflexivityof linear topological spaces, Math. Annalen 164 (1966) 280-285.
  • [14] J. R. Retherford and C. W. McArthur, Some remarks on bases in linear topo- logical spaces, Math. Annalen 164 (1966) 38-41.
  • [15] L. J. Weill, Stabilityof bases in complete barrelled spaces Proc. Amer. Math. Soc. 18 (1967), 1045-1050.