Bulletin of the American Mathematical Society

Approximation numbers and Kolmogoroff diameters of bounded linear operators

C. V. Hutton, J. S. Morrell, and J. R. Retherford

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 80, Number 3 (1974), 462-466.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183535519

Mathematical Reviews number (MathSciNet)
MR0336391

Zentralblatt MATH identifier
0295.47008

Subjects
Primary: 47A30: Norms (inequalities, more than one norm, etc.) 47B05 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

Citation

Hutton, C. V.; Morrell, J. S.; Retherford, J. R. Approximation numbers and Kolmogoroff diameters of bounded linear operators. Bull. Amer. Math. Soc. 80 (1974), no. 3, 462--466. https://projecteuclid.org/euclid.bams/1183535519


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References

  • 1. I. C. Gohberg and M. G. Kreĭn, Introduction to the theory of linear nonself-adjoint operators in Hilbert space, "Nauka, " Moscow, 1965; English transl., Transl. Math. Monographs, vol. 18, Amer. Math. Soc. Providence, R.I., 1969. MR 36 #3137; 39 #7447.
  • 2. A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 17, 763.
  • 3. P. Johnson, Thesis, University of Michigan, Ann Arbor, Mich., 1973.
  • 4. J. Lindenstrauss and A. Pelczyński, Absolutely summing operators in Lp-spaces and their applications, Studia Math. 29 (1968), 275-326. MR 37 #6743.
  • 5. A. S. Markus, Some criteria for the completeness of a system of root vectors of a linear operator in a Banach space, Mat. Sb. 70 (112) (1966), 526-561; English transl., Amer. Math. Soc. Transl. (2) 85 (1969), 51-91. MR 35 #7151.
  • 6. A. S. Markus and V. I.Macaev, Analogs of Weyl inequalities and trace theorems in a Banach space, Mat. Sb. 86 (128) (1971), 299-313 = Math. USSR Sb. 15 (1971), 299-334. MR 45 #7512.
  • 7. B. S. Mitjagin and A. Pelczyński, Nuclear operators and approximative dimension, Proc. Internat. Congr. Math. (Moscow, 1966), "Mir, " Moscow, 1968, pp. 366-372; English transl., Amer. Math. Soc. Transl. (2) 70 (1968), 137-145. MR 39 #6046.
  • 8. A. Pietsch, Einige neue Klassen von kompakten linearen Abbildungen, Rev. Math. Pures Appl. (Bucharest), 8 (1963), 427-447. MR 31 #3874.