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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Authors: G. R. Belitskii and Yu. I. Lyubich
Title: Matrix norms and their applications
Additional book information: Translated by A. Iacob. Oper. Theory: Adv. Appl., vol. 36, Birkhäuser, Basel, Boston, Berlin, 1988, viii+209 pp., $87.50. ISBN 0-8176-2220-9.

References [Enhancements On Off] (What's this?)

  • 1. I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726
  • 2. I. Gelfand and M. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197–213 (English, with Russian summary). MR 0009426
  • 3. Jan Mařík and Vlastimil Pták, Norms, spectra and combinatorial properties of matrices, Czechoslovak Math. J 10 (85) (1960), 181–196 (English, with Russian summary). MR 0120243
  • 4. F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, https://doi.org/10.2307/1968693
  • 5. J. von Neumann, Some matrix-inequalities and metrization of matric-space, Tomsk Univ. Rev. 1 (1937), 286-300; also Collected works, vol. IV, Pergamon (1962), 205-219.
  • 6. Robert Schatten, A Theory of Cross-Spaces, Annals of Mathematics Studies, no. 26, Princeton University Press, Princeton, N. J., 1950. MR 0036935
  • 7. Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete. N. F., Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0119112

Review Information:

Reviewer: Peter A. Fillmore
Journal: Bull. Amer. Math. Soc. 23 (1990), 620-623
DOI: https://doi.org/10.1090/S0273-0979-1990-16005-7