Bulletin of the American Mathematical Society

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Book Information:

Author: 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.

[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)

Per Enflo, A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309–317. MR 402468, DOI 10.1007/BF02392270

Alexandre Grothendieck, Sur une notion de produit tensoriel topologique d’espaces vectoriels topologiques, et une classe remarquable d’espaces vectoriels liée à cette notion, C. R. Acad. Sci. Paris 233 (1951), 1556–1558 (French). MR 52029

Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539

J. R. Holub, Tensor product mappings, Math. Ann. 188 (1970), 1–12. MR 284828, DOI 10.1007/BF01435409

J. R. Holub, Tensor product mappings. II, Proc. Amer. Math. Soc. 42 (1974), 437–441. MR 331104, DOI 10.1090/S0002-9939-1974-0331104-4

N. J. Kalton, Unusual traces on operator ideals, Math. Nachr. 134 (1987), 119–130. MR 918672, DOI 10.1002/mana.19871340108

Hermann König, Eigenvalue distribution of compact operators, Operator Theory: Advances and Applications, vol. 16, Birkhäuser Verlag, Basel, 1986. MR 889455, DOI 10.1007/978-3-0348-6278-3

Hermann König, $s$-numbers, eigenvalues and the trace theorem in Banach spaces, Studia Math. 67 (1980), no. 2, 157–172. MR 583296, DOI 10.4064/sm-67-2-157-172

V. B. Lidskiĭ, Non-selfadjoint operators with a trace, Dokl. Akad. Nauk SSSR 125 (1959), 485–487 (Russian). MR 0105023

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

A. Pietsch, Eigenvalues and $s$-numbers, Mathematik und ihre Anwendungen in Physik und Technik [Mathematics and its Applications in Physics and Technology], vol. 43, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987. MR 917067

Albrecht Pietsch, $s$-numbers of operators in Banach spaces, Studia Math. 51 (1974), 201–223. MR 361883, DOI 10.4064/sm-51-3-201-223

Albrecht Pietsch, Weyl numbers and eigenvalues of operators in Banach spaces, Math. Ann. 247 (1980), no. 2, 149–168. MR 568205, DOI 10.1007/BF01364141

Albrecht Pietsch, Operator ideals with a trace, Math. Nachr. 100 (1981), 61–91. MR 632621, DOI 10.1002/mana.19811000105

A. Pietsch, Zur Fredholmschen Theorie in lokalkonvexen Räumen, Studia Math. 22 (1962/63), 161–179 (German). MR 144226, DOI 10.4064/sm-22-2-161-179

J. R. Retherford, Trace, Special topics of applied mathematics (Proc. Sem., Ges. Math. Datenverarb., Bonn, 1979) North-Holland, Amsterdam-New York, 1980, pp. 47–56. MR 585149

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, DOI 10.1112/plms/s2-53.2.109

Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149

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, DOI 10.1073/pnas.35.7.408

[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. MR 0402468




[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. MR 52029




[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