Bulletin of the American Mathematical Society

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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.

I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726

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

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 120243

F. J. Murray and J. Von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), no. 1, 116–229. MR 1503275, DOI 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.

Robert Schatten, A Theory of Cross-Spaces, Annals of Mathematics Studies, No. 26, Princeton University Press, Princeton, N. J., 1950. MR 0036935

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

1.

I. M. Gelfand, Normierte ringe, Mat. Sb. 9 (1941), 3-24. MR 0004726

2.

I. M. Gelfand and M. A. Naimark, On the embedding of normed rings into the ring of operators in Hilbert space, Mat. Sb. 12 (1943), 197-213. MR 9426

3.

J. Marik and V. Ptak, Norms, spectra, and combinatorial properties of matrices, Czechoslovak Math. J. 10 (1960), 181-196. MR 120243

4.

F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. 37(1936), 116-229. MR 1503275

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.

R. Schatten, A theory of cross-spaces, Ann. of Math. Stud., no. 26, Princeton Univ. Press, Princeton, N. J., 1950. MR 36935

7.

R. Schatten, Norm ideals of completely continuous operators, Ergeb. Math. Grenzgeb., Springer-Verlag, New York, 1960. MR 119112