Measures from Dixmier traces and zeta functions

Journal of Functional Analysis

Volumn 259, Issue 8, 2010, Pages 1915-1949

  Lord, Steven ^a,b   Potapov, Denis ^b   Sukochev, Fedor ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Dixmier trace; Lebesgue integral; Noncommutative geometry; Noncommutative integral; Noncommutative residue; Zeta functions

Indexed keywords

EID: 77955518510     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2010.06.012     Document Type: Article

References (28)

1. Benameuar M.-T., Fack T. Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras. Adv. Math. 2006, 199:29-87.
2. Bergh J., Löfström J. Interpolation Spaces, an Introduction. Grundlehren Math. Wiss. 1976, vol. 223. Springer-Verlag, Berlin, Heidelberg, New York.
3. Bikchentaev A. Majorization for products of measurable operators. Internat. J. Theoret. Phys. 1998, 37(1):571-576.
4. Bikchentaev A.M. On a property of Lp spaces on semifinite von Neumann algebras. Math. Notes 1998, 64(1-2):159-163.
5. Bratteli O., Robinson D.W. Operator Algebras and Quantum Statistical Mechanics 1. Texts Monogr. Phys. 1987, Springer-Verlag, Heidelberg. 2nd edition.
6. Carey A., Phillips J., Sukochev F.A. Spectral flow and Dixmier traces. Adv. Math. 2003, 173:68-113.
7. Carey A., Potapov D., Sukochev F. Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators URL:. http://arxiv.org/abs/0807.2129v2.
8. Carey A., Rennie A., Sedaev A., Sukochev F.A. The Dixmier trace and asymptotics of zeta functions. J. Funct. Anal. 2007, 249:253-283.
9. Carey A., Sukochev F.A. Dixmier traces and some applications in non-commutative geometry. Russian Math. Surveys 2006, 61:1039-1099.
10. Connes A. The action functional in non-commutative geometry. Comm. Math. Phys. 1988, 117:673-683.
11. Connes A. Noncommutative Geometry 1994, Academic Press, New York.
12. Connes A., Moscovici H. The local index formula in noncommutative geometry. Geom. Funct. Anal. 1995, 5:174-243.
13. Dixmier J. Existence de traces non normales. C. R. Acad. Sci. Paris 1966, 262:A1107-A1108.
14. Fack T. Singular traces in N.C.G. Educational Week on Noncommutative Integration, Thomas Stieltjes Institute for Mathematics. http://www.math.leidenuniv.nl/~mdejeu/NoncomIntWeek_2008_Fack_singular_traces_in_NCG.pdf.
15. Gayral V., Iochum B., Várilly J. Dixmier traces on noncompact isospectral deformations. J. Funct. Anal. 2006, 237:507-539.
16. Gohberg I.C., Kreǐn M.G. Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v Gilbertovom prostranstve 1965, Izdat. "Nauka", Moscow.
17. Gracia-Bondía J.M., Várilly J.C., Figueroa H. Elements of Noncommutative Geometry. Birkhäuser Adv. Texts 2001, Birkhäuser, Boston.
18. Hawkins E. Hamiltonian gravity and noncommutative geometry. Comm. Math. Phys. 1997, 187(2):471-489.
19. Landi G. An Introduction to Noncommutative Spaces and Their Geometries. Lecture Notes in Phys. 1998, vol. 51. Springer-Verlag, Berlin.
20. Lord S., Sedaev A., Sukochev F.A. Dixmier traces as singular symmetric functionals and applications to measurable operators. J. Funct. Anal. 2005, 244(1):72-106.
21. S. Lord, F.A. Sukochev, Noncommutative residues and a characterisation of the noncommutative integral, Proc. Amer. Math. Soc. (2010), doi:10.1090/S0002-9939-2010-10472-0.
22. *-Algebras and Their Automorphism Groups. London Math. Soc. Monogr. 1979, vol. 14. Academic Press, London.
23. Reed M., Simon B. Methods of Modern Mathematical Physics, vol. I: Functional Analysis 1980, Academic Press, San Diego, London. revised and enlarged edition.
24. ∞. Studia Math. 1972, 44:219-227.
25. Segal I.E. A non-commutative extension of abstract integration. Ann. Math. 1953, 57:401-457.
26. Simon B. Trace Ideals and Their Applications. Math. Surveys Monogr. 2005, vol. 120. Amer. Math. Soc.
27. Takesaki M. Theory of Operator Algebras I (Operator Algebras and Non-Commutative Geometry V). Encyclopaedia Math. Sci. 2002, vol. 124. Springer-Verlag, Berlin.
28. Wodzicki M. Local invariants of spectral asymmetry. Invent. Math. 1984, 75:143-178.