Pacific Journal of Mathematics

Absolutely divergent series and isomorphism of subspaces.

William H. Ruckle

Article information

Source
Pacific J. Math., Volume 58, Number 2 (1975), 605-615.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102905692

Mathematical Reviews number (MathSciNet)
MR0390729

Zentralblatt MATH identifier
0316.46012

Subjects
Primary: 46B15: Summability and bases [See also 46A35]

Citation

Ruckle, William H. Absolutely divergent series and isomorphism of subspaces. Pacific J. Math. 58 (1975), no. 2, 605--615. https://projecteuclid.org/euclid.pjm/1102905692


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References

  • [1] A. Dvoretzky, Some results on convex bodies and Banach spaces, Proc. Symp. on Linear spaces, Jerusalem (1961), 123-160.
  • [2] A. Dvoretzky and C. A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. U.S.A., 36 (1950), 192-197.
  • [3] A. Grothendieck, Sur certaines classes de suites dans lea espaces de Banach, et le thoreme de Dvoretzky-Rogers, Bol. Soc. Matem. Sao Paulo, 8 (1956), 81-110.
  • [4] W. B. Johnson, H. P. Rosenthal, and M. Zippin, On bases finite dimensionaldecompositions and weaker structures in Banach spaces, Israel J. Math., 9 (1971), 488-506.
  • [5] N. J. Kalton, and W. H. Ruckle, A series characterization of subspaces of Lp (u) spaces, Bull. Amer. Math. Soc, 79 (1973), 1019-1022.
  • [6] J. Londenstrauss, and A. Pelczynski, Absolutely summing operators in Lp spaces and their applications, Studia Math., 29 (1968), 275-336.
  • [7] V. J. Mizel, and K. Sundaresan, Banach sequence spaces, Arch. Math. (Basel), 19 (1968), 59-69.
  • [8] A. Pietsch, Absolut p-summierende Abbildungen in normierten Rumen, Studia Math., 28 (1967), 333-353.
  • [9] P. Saphar, Une caracterisation des soun-espaces de Lp et ses applications, C. R. de L' Accd. des Sci., 227 (1973), 35-39.

See also

  • II : William H. Ruckle. Absolutely divergent series and isomorphism of subspaces. II. Pacific Journal of Mathematics volume 68, issue 1, (1977), pp. 229-240.