Bulletin (New Series) of the American Mathematical Society

Review: Albrecht Pietsch, Eigenvalues and $s$-numbers

J. R. Retherford

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.), Volume 19, Number 2 (1988), 531-538.

First available in Project Euclid: 4 July 2007

Permanent link to this document


Retherford, J. R. Review: Albrecht Pietsch, Eigenvalues and $s$- numbers. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 531--538. https://projecteuclid.org/euclid.bams/1183554745

Export citation


  • [A] D. Eh. Allakhverdiev, On the rate of approximation of completely continuous operators by finite dimensional operators, Azerbajzhan Gos. Univ. Uchen. Zap. (Baku) 2 (1957), 27-37. (Russian)
  • [E] P. Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309-317.
  • [G1] A. Grothendieck, Sur une notion de produit tensoriels topologique d'espaces vectoriels topologiques, et une classe remarquable d'espaces vectoriels liées à cette notion, C. R. Acad. Sci. Paris 233 (1951), 1556-1558.
  • [G2] A. Grothendieck, Produits tensoriels topologiques et espaces nuclearies, Mem. Amer. Math. Soc., no. 16, Amer. Math. Soc., Providence, R. I., 1955.
  • [H1] J. R. Holub, Tensor product mappings, Math. Ann. 188 (1970), 1-12.
  • [H2] J. R. Holub, Tensor product mappings, Proc. Amer. Math. Soc. 42 (1974), 437-441.
  • [K] N. Kalton, Unusual traces on operator ideals, Math. Nachr. (to appear).
  • [Kö1] H. König, Eigenvalue distribution of compact operators, Birkhauser Verlag, Stuttgart, 1986.
  • [Kö2] H. König, s-numbers, eigenvalues and the trace theorem in Banach spaces, Studia Math. 67 (1980), 157-172.
  • [L] V. B. Lidskii, Non-self-adjoint operators with a trace, Dokl. Akad. Nauk SSSR 125 (1959), 485-487. (Russian)
  • [M] F. J. Murray and John von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229.
  • [P1] A. Pietsch, Eigenvalues and s-numbers, Cambridge Studies in Advanced Mathematics 13 (under review).
  • [P2] A. Pietsch, s-numbers of operators in Banach spaces, Studia Math. 51 (1974), 201-223.
  • [P3] A. Pietsch, Weyl numbers and eigenvalues of operators in Banach spaces, Math. Ann. 247 (1980), 149-168.
  • [P4] A. Pietsch, Operator ideals with a trace, Math. Nachr. 100 (1981), 61-91.
  • [P5] A. Pietsch, Zur Fredholmschen Theorie in lokal Konvexen Raumen, Studia Math. 22 (1963), 161-179.
  • [R] J. R. Retherford, Trace, Proc Sem. Ges. Math. Datenverarb., Special Topics of Applied Mathematics, North-Holland, 1979, pp. 47-56.
  • [Ru] A. F. Ruston, On the Fredholm theory of integral equations for operators belonging to the trace class of a general Banach space, Proc. London Math. Soc. (2) 53 (1951), 109-124.
  • [S] Barry Simon, Trace Ideals and their applications, London Math. Soc. Lecture Notes 35, Cambridge Univ. Press, 1979.
  • [W] Hermann Weyl, Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 408-411.