The Dixmier trace and asymptotics of zeta functions

Journal of Functional Analysis

Volumn 249, Issue 2, 2007, Pages 253-283

  Carey, Alan L ^a   Rennie, Adam ^b   Sedaev, Aleksandr ^c   Sukochev, Fyodor ^d  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

^c VORONEZH STATE TECHNICAL UNIVERSITY   (Russian Federation)

^d FLINDERS UNIVERSITY   (Australia)

Author keywords

Dixmier trace; Spectral triple; Zeta function

Indexed keywords

EID: 34250682687     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.04.011     Document Type: Article

References (40)

1. Benameur M.-T., and Fack T. Type II noncommutative geometry. I. Dixmier trace in von Neumann algebras. Adv. Math. 199 (2006) 29-87
2. Benameur M.T., Carey A.L., Phillips J., Rennie A., Sukochev F.A., and Wojciechowski K.P. Analytic formulae for spectral flow in von Neumann algebras. In: Booss-Bavnbek B., Klimek S., Lesch M., and Zhang W. (Eds). Analysis, Geometry and Topology of Elliptic Operators (2006), World Sci. Publishing, Singapore
3. Carey A.L., and Phillips J. Spectral flow in Θ-summable Fredholm modules, eta invariants and the JLO cocycle. K-Theory 31 (2004) 135-194
4. Carey A.L., Phillips J., and Sukochev F.A. Spectral flow and Dixmier traces. Adv. Math. 173 (2003) 68-113
5. Carey A.L., Phillips J., Rennie A., and Sukochev F. The local index formula in semifinite von Neumann algebras I. Spectral flow. Adv. Math. 202 (2006) 451-516
6. Carey A.L., Phillips J., Rennie A., and Sukochev F. The local index formula in semifinite von Neumann algebras II: The even case. Adv. Math. 202 (2006) 517-554
7. Chakraborty P.S., and Pal A. Equivariant spectral triples on the quantum SU (2) group. K-Theory 30 (2003) 107-126
8. q (2). math/0501019
9. Chamseddine A., and Connes A. The spectral action principle. Comm. Math. Phys. 186 (1997) 731-750
10. Cipriani F., Guido E., and Scarlatti S. A remark on trace properties of K-cycles. J. Operator Theory 35 (1996) 179-189
11. Chilin V.I., and Sukochev F.A. Weak convergence in noncommutative symmetric spaces. J. Operator Theory 31 (1994) 35-65
12. Connes A. Noncommutative Differential Geometry. Publ. Math. Inst. Hautes Études Sci. 62 (1985) 1-44
13. Connes A. The action functional in noncommutative geometry. Comm. Math. Phys. 117 (1988) 673-683
14. Connes A. Traces de Dixmier, modules de Fredholm et geometrie Riemannienne. Conformal Field Theories and Related Topics, Annecy-le-Vieux, 1988. Nuclear Phys. B Proc. Suppl. 5b (1988) 65-70
15. Connes A. Noncommutative Geometry (1994), Academic Press, San Diego, CA
16. Connes A. Geometry from the spectral point of view. Lett. Math. Phys. 34 (1995) 203-238
17. Connes A., and Lott J. Particle models and noncommutative geometry. Nuclear Phys. B 18 Suppl. (1991) 29-47
18. Connes A., and Marcolli M. A walk in the noncommutative garden. math.QA/0601054
19. q (2). Comm. Math. Phys. 259 (2005) 729-759
20. Dixmier J. Existence de traces non normales. C. R. Acad. Sci. Paris 262 (1966) 1107-1108 (in French)
21. Dodds P.G., Dodds T.K., and de Pagter B. Non-commutative Banach function spaces. Math. Z. 201 (1989) 583-597
22. Dodds P.G., de Pagter B., Semenov E.M., and Sukochev F.A. Symmetric functionals and singular traces. Positivity 2 (1998) 47-75
23. Dodds P.G., de Pagter B., Sedaev F.A., Semenov E.M., and Sukochev F.A. Singular symmetric functionals and Banach limits with additional invariance properties. Izv. Ross. Akad. Nauk, Ser. Mat. 67 (2003) 111-136 (in Russian)
24. Dodds P.G., de Pagter B., Sedaev F.A., Semenov E.M., and Sukochev F.A. Singular symmetric functionals. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 290 (2002) 42-71, 178, Issled. po Linein. Oper. i Teor. Funkts. 30 (in Russian); translation in:
25. Dodds P.G., de Pagter B., Sedaev F.A., Semenov E.M., and Sukochev F.A. Singular symmetric functionals. J. Math. Sci. (N.Y.) 124 (2004) 4867-4885
26. Fack T. Sur la notion de valeur caractéristique. J. Operator Theory 7 (1982) 307-333
27. Fack T., and Kosaki H. Generalised s-numbers of τ-measurable operators. Pacific J. Math. 123 (1986) 269-300
28. Gayral V. Heat kernel approach to UV/IR mixing on isospectral deformation manifolds. hep-th/0412233
29. Gayral V., Gracia-Bondía J.M., Iochum B., Schücker T., and Várilly J.C. Moyal planes are spectral triples. Comm. Math. Phys. 246 (2004) 569-623
30. Gohberg I.C., and Kreǐn M.G. Introduction to the Theory of Non-selfadjoint Operators. Transl. Math. Monogr. vol. 18 (1969), Amer. Math. Soc., Providence, RI
31. Kreǐn S.G., Petunīn Yu.I., and Semenov E.M. Interpolyatsiya lineǐnykh operatorov. (in Russian). Interpolation of Linear Operators. Transl. Math. Monogr. vol. 54 (1982), Amer. Math. Soc., Providence, RI translated by J. Szu{combining double acute accent}cs
32. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces. I. Sequence Spaces. Results Math. vol. 92 (1977), Springer-Verlag, Berlin
33. Lindenstrauss J., and Tzafriri L. Classical Banach Spaces. II. Function Spaces. Results Math. vol. 97 (1979), Springer-Verlag, Berlin
34. Lord S., Sedaev A., and Sukochev F. Dixmier traces as singular symmetric functionals and applications to measurable operators. J. Funct. Anal. 224 1 (2005) 72-106
35. n. Math. Phys. Anal. Geom. 6 (2003) 89-105
36. *-algebras I: The index theorem. J. Funct. Anal. 233 (2006) 92-134
37. *-algebras. math.oa/0512438
38. D. Potapov, Lipschitz and commutator estimates, a unified approach, PhD thesis, Flinders University of South Australia
39. D. Potapov, F.A. Sukochev, Lipschitz and commutator estimates in symmetric operator spaces, J. Operator Theory, in press
40. Sukochev F.A. Operator estimates for Fredholm modules. Canad. J. Math. 52 (2000) 849-896