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Book Information

Author(s): Albrecht Pietsch
Title: Eigenvalues and $s$-numbers
Additional book information: Akademische Verlagsgesellschaft Geest and Portig K.-G., Leipzig, and Cambridge University Press, Cambridge, New York and Melbourne, 1987 (Cambridge Studies in Advanced Mathematics, vol. 13) 360 pp., $59.50. ISBN 0-521-32532-3

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[G2] A. Grothendieck, Produits tensoriels topologiques et espaces nuclearies, Mem. Amer. Math. Soc., no. 16, Amer. Math. Soc., Providence, R. I., 1955. MR 75539

[H1] J. R. Holub, Tensor product mappings, Math. Ann. 188 (1970), 1-12. MR 284828

[H2] J. R. Holub, Tensor product mappings, Proc. Amer. Math. Soc. 42 (1974), 437-441. MR 331104

[K] N. Kalton, Unusual traces on operator ideals, Math. Nachr. (to appear). MR 918672

[Kö1] H. König, Eigenvalue distribution of compact operators, Birkhauser Verlag, Stuttgart, 1986. MR 889455

[Kö2] H. König, s-numbers, eigenvalues and the trace theorem in Banach spaces, Studia Math. 67 (1980), 157-172. MR 583296

[L] V. B. Lidskii, Non-self-adjoint operators with a trace, Dokl. Akad. Nauk SSSR 125 (1959), 485-487. (Russian) MR 105023

[M] F. J. Murray and John von Neumann, On rings of operators, Ann. of Math. (2) 37 (1936), 116-229. MR 1503275

[P1] A. Pietsch, Eigenvalues and s-numbers, Cambridge Studies in Advanced Mathematics 13 (under review). MR 890520

[P2] A. Pietsch, s-numbers of operators in Banach spaces, Studia Math. 51 (1974), 201-223. MR 361883

[P3] A. Pietsch, Weyl numbers and eigenvalues of operators in Banach spaces, Math. Ann. 247 (1980), 149-168. MR 568205

[P4] A. Pietsch, Operator ideals with a trace, Math. Nachr. 100 (1981), 61-91. MR 632621

[P5] A. Pietsch, Zur Fredholmschen Theorie in lokal Konvexen Raumen, Studia Math. 22 (1963), 161-179. MR 144226

[R] J. R. Retherford, Trace, Proc Sem. Ges. Math. Datenverarb., Special Topics of Applied Mathematics, North-Holland, 1979, pp. 47-56. MR 585149

[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. MR 42612

[S] Barry Simon, Trace Ideals and their applications, London Math. Soc. Lecture Notes 35, Cambridge Univ. Press, 1979. MR 541149

[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. MR 30693

Review Information:
Journal: Bull. Amer. Math. Soc. 19 (1988), 531-538.
DOI: 10.1090/S0273-0979-1988-15732-1
PII: S 0273-0979(1988)15732-1

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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