Pacific Journal of Mathematics

Some metrics on the subspaces of a Banach space.

Earl Berkson

Article information

Source
Pacific J. Math., Volume 13, Number 1 (1963), 7-22.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103035953

Mathematical Reviews number (MathSciNet)
MR0152869

Zentralblatt MATH identifier
0118.10402

Subjects
Primary: 46.10

Citation

Berkson, Earl. Some metrics on the subspaces of a Banach space. Pacific J. Math. 13 (1963), no. 1, 7--22. https://projecteuclid.org/euclid.pjm/1103035953


Export citation

References

  • [1] N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert- Raum, Akademie Verlag, Berlin, 1954.
  • [2] J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc, 40 (1936), 396-414.
  • [3] I. C. Gochberg and M. G. Krein, Fundamentalaspects of defect numbers, root numbers, and indexes of linear operators, Uspekhi Mat. Nauk., 12, 2(74) (1957), 43-118 (in Russian).
  • [4] I. C. Gochberg and A. S. Markus, Two theorems on the opening between subspaces of a Banach space, Uspekhi Mat. Nauk., 89 (1959), 135-140 (in Russian).
  • [5] P. R. Halmos and G. Lumer, Square roots of operators II, Proc. Amer. Math. Soc, 5 (1954), 589-595.
  • [6] F. Hausdorff, Mengenlehre, Dover, New York, 1944.
  • [7] E. Hille and R. S. Phillips, Functional Analysis qt,ndSqmi-Groups, Amer, Math. Soc. Colioq. Publ,, 31 (1957).
  • [8] M. G. Krein and M. A. Krasnoselsk, Fundamental theorems concerning the exten- sion of Hermitian operators and some of their applications to the theory of orthogonal polynomials and the moment problem, Uspekhi Mat. Nauk., 2, 3 (1947) (in Russian).
  • [9] M. G. Krein, M. A. Krasnoselski, and D. P. Milman, Concerning the deficiency numbers of linear operators in Banach space and some geometric questions, Sbornik Trudov Inst. A. N. Ukr. S. S. R., 11 (1948) (in Russian).
  • [10] C. Kuratowski, Topologie I. Monograf je Matematyczne, Warsaw-Lwow, 1933.
  • [11] J. L. Massera and J. J. Schaffer, Linear differentialequations andfunctional analysis, I, Annals of Math., 67 (1958), 517-573.
  • [12] J. D. Newburgh, A topology for closedoperators, Annals of Math., 53 (1951),250-255.
  • [13] A. E. Taylor, Introduction to Functional Analysis, John Wiley, New York, 1958.