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ЖУРНАЛЫ // Moscow Mathematical Journal

Mosc. Math. J., 2002, том 2, номер 4, страницы 769–798 (Mi mmj72)

Vestigia investiganda
M. Wodzicki

Список литературы

1. S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti, “Nonstandard representation of nonnormal traces”, Dynamics of complex and irregular systems (Bielefeld, 1991), Bielefeld Encount. Math. Phys., VIII, World Sci. Publishing, River Edge, NJ, 1993, 1–11  mathscinet
2. S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti, “Singular traces and nonstandard analysis”, Advances in analysis, probability and mathematical physics (Blaubeuren, 1992), Math. Appl., 314, Kluwer Acad. Publ., Dordrecht, 1995, 3–19  mathscinet  zmath
3. S. Albeverio, D. Guido, A. Ponosov, S. Scarlatti, “Singular traces and compact operators”, J. Funct. Anal., 137:2 (1996), 281–302  crossref  mathscinet  zmath
4. N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Encyclopedia of Mathematics and its Applications, 27, Cambridge University Press, Cambridge, 1987  mathscinet  zmath
5. R. Bojanic, E. Seneta, “A unified theory of regularly varying sequences”, Math. Z., 134 (1973), 91–106  crossref  mathscinet  zmath
6. N. Bourbaki, Éléments de mathématique. Première partie. (Fasc. II.) Livre III: Topologie générale, Chap. 1–2, Hermann, Paris, 1961  mathscinet
7. J. W. Calkin, “Two-sided ideals and congruences in the ring of bounded operators in Hilbert space”, Ann. of Math. (2), 42 (1941), 839–873  crossref  mathscinet  zmath
8. A. H. Chamseddine and A. Connes, “Universal formula for noncommutative geometry actions: unification of gravity and the standard model”, Phys. Rev. Lett., 77:24 (1996), 4868–4871  crossref  mathscinet  zmath  adsnasa
9. A. Connes, “Trace de Dixmier, modules de Fredholm et géométrie riemannienne”, Conformal field theories and related topics (Annecy-le-Vieux, 1988), Nuclear Phys. B Proc. Suppl., 5B (1988), 65–70  crossref  mathscinet  zmath  adsnasa
10. A. Connes, “Essay on physics and noncommutative geometry”, The interface of mathematics and particle physics (Oxford, 1988), Inst. Math. Appl. Conf. Ser. New Ser., 24, Oxford Univ. Press, New York, 1990, 9–48  mathscinet
11. A. Connes, Noncommutative geometry, Academic Press Inc., San Diego, CA, 1994  mathscinet  zmath
12. A. Connes, “Geometry from the spectral point of view”, Lett. Math. Phys., 34:3 (1995), 203–238  crossref  mathscinet  zmath  adsnasa
13. A. Connes, “Noncommutative geometry and reality”, J. Math. Phys., 36:11 (1995), 6194–6231  crossref  mathscinet  zmath  adsnasa
14. A. Connes, “Brisure de symétrie spontanée et géométrie du point de vue spectral”, Exp. No. 816, Séminaire Bourbaki, Vol. 1995/96, Astérisque, 241, no. 5, 1997, 313–349  mathscinet  zmath; J. Geom. Phys., 23:3–4 (1997), 206–234  crossref  mathscinet  zmath  adsnasa
15. A. Connes, J. Lott, “Particle models and noncommutative geometry”, Recent advances in field theory (Annecy-le-Vieux, 1990), Nuclear Phys. B Proc. Suppl., 18B (1990) (1991), 29–47  crossref  mathscinet  adsnasa
16. A. Connes, J. Lott, “The metric aspect of noncommutative geometry”, New symmetry principles in quantum field theory (Cargèse, 1991), NATO Adv. Sci. Inst. Ser. B Phys., 295, Plenum, New York, 1992, 53–93  mathscinet
17. J. Dixmier, “Existence de traces non normales”, C. R. Acad. Sci. Paris Sér. A-B, 262 (1966), A1107–A1108  mathscinet
18. K. Dykema, T. Figiel, G. Weiss, M. Wodzicki, Commutator structure of operator ideals, submitted  mathscinet
19. K. Dykema, G. Weiss, M. Wodzicki, “Unitarily invariant trace extensions beyond the trace class”, Complex analysis and related topics (Cuernavaca, 1996), Oper. Theory Adv. Appl., 114, Birkhäuser, Basel, 2000, 59–65  mathscinet  zmath
20. E. Fischer, “Über quadratische Formen mit reellen Koeffizienten”, Monatsh. Math. Phys., 16 (1905), 234–249  crossref  mathscinet  zmath
21. J. Galambos, E. Seneta, “Regularly varying sequences”, Proc. Amer. Math. Soc., 41 (1973), 110–116  crossref  mathscinet  zmath
22. I. C. Gohberg, M. G. Krein, Introduction to the theory of linear nonselfadjoint operators, Izdat. “Nauka”, Moscow, 1965 (Russian)  mathscinet; English translation in: Translations of Mathematical Monographs, 18, Amer. Math. Soc., Providence, R.I., 1969  mathscinet  zmath
23. D. Guido, T. Isola, “Singular traces and their applications to geometry”, Operator algebras and quantum field theory (Rome, 1996), Internat. Press, Cambridge, MA, 1997, 440–456  mathscinet  zmath
24. P. R. Halmos, “Commutators of operators”, Amer. J. Math., 74 (1952), 237–240  crossref  mathscinet  zmath
25. U. Hebisch, H. J. Weinert, “Semirings and semifields”, Handbook of algebra, Vol. 1, North-Holland, Amsterdam, 1996, 425–462  mathscinet  zmath
26. N. J. Kalton, “Unusual traces on operator ideals”, Math. Nachr., 134 (1987), 119–130  crossref  mathscinet  zmath
27. N. J. Kalton, “Trace-class operators and commutators”, J. Funct. Anal., 86:1 (1989), 41–74  crossref  mathscinet  zmath
28. J. Karamata, “Sur certains “Tauberian theorems” de M. M. Hardy et Littlewood”, Mathematica (Cluj), 3 (1930), 33–48  zmath
29. R. Nest, E. Schrohe, “Dixmier's trace for boundary value problems”, Manuscripta Math., 96:2 (1998), 203–218  crossref  mathscinet  zmath
30. OMEROS, ODUSSEIA, Ionia, 725 BC
31. A. Pietsch, “Operator ideals with a trace”, Math. Nachr., 100 (1981), 61–91  crossref  mathscinet  zmath
32. A. Pietsch, Eigenvalues and $s$-numbers, Mathematik und ihre Anwendungen in Physik und Technik [Mathematics and its Applications in Physics and Technology], 43, Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig, 1987  mathscinet; Cambridge Studies in Advanced Mathematics, 13, Cambridge University Press, Cambridge, 1987  mathscinet  zmath
33. J. V. Varga, “Traces on irregular ideals”, Proc. Amer. Math. Soc., 107:3 (1989), 715–723  crossref  mathscinet  zmath
34. G. Weiss, Commutators and operator ideals, Ph.D. thesis, University of Michigan, Ann Arbor, 1975  zmath
35. G. Weiss, “Commutators of Hilbert–Schmidt operators. II”, Integral Equations Operator Theory, 3:4 (1980), 574–600  crossref  mathscinet  zmath
36. G. Weiss, “Commutators of Hilbert–Schmidt operators. I”, Integral Equations Operator Theory, 9:6 (1986), 877–892  crossref  mathscinet  zmath
37. M. Wodzicki, “Local invariants of spectral asymmetry”, Invent. Math., 75:1 (1984), 143–177  crossref  mathscinet
38. M. Wodzicki, “Noncommutative residue. I. Fundamentals”, $K$-theory, arithmetic and geometry (Moscow, 1984–1986), Lecture Notes in Math., 1289, Springer, Berlin, 1987, 320–399  mathscinet
39. M. Wodzicki, “Algebraic $K$-theory and functional analysis”, First European Congress of Mathematics, Vol. II (Paris, 1992), Progr. Math., 120, Birkhäuser, Basel, 1994, 485–496  mathscinet  zmath
40. M. Wodzicki, Algebraic $K$-theory of operator ideals, in preparation


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