The Hochschild class of the Chern character for semifinite spectral triples

Journal of Functional Analysis

Volumn 213, Issue 1, 2004, Pages 111-153

  Carey, Alan L ^a   Phillips, John ^b   Rennie, Adam ^c   Sukochev, Fyodor A ^d  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF VICTORIA   (Canada)

^c UNIVERSITY OF NEWCASTLE   (Australia)

^d FLINDERS UNIVERSITY   (Australia)

Author keywords

Chern character; Cyclic cohomology; Fredholm module; Von Neumann algebra

Indexed keywords

EID: 3042759267     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.11.016     Document Type: Article

References (28)

1. M.-T. Benameur T. Fack On von Neumann Spectral Triples, arxiv posting: math.KT/0012233.
2. Birman M.S. Koplienko L.S. Solomyak M.Z. Estimates for the spectrum of the difference between fractional powers of two selfadjoint operators Soviet Math. 19 3 1975 1-6
3. Carey A.L. Phillips J. Unbounded Fredholm modules and spectral flow Canad. J. Math. 50 4 1998 673-718
4. Carey A.L. Phillips J. Theta summable Fredholm modules, eta invariants and the JLO cocycle K-Theory 30 2 2004 135-194
5. Carey A.L. Phillips J. Sukochev F.A. On unbounded p-summable Fredholm modules Adv. Math. 151 2000 140-163
6. Carey A.L. Phillips J. Sukochev F.A. Spectral flow and dixmier traces Adv. Math. 173 2003 68-113
7. Chilin V.I. Sukochev F.A. Weak convergence in operator spaces J. Oper. Theory 31 1991 35-65
8. Cipriani F. Guido D. Scarlatti S. A remark on trace properties of K-cycles J. Oper. Theory 35 1996 179-189
9. Connes A. Noncommutative differential geometry Publ. Math. IHES 39 1985 257-360
10. Connes A. Noncommutative Geometry 1994 Academic Press New York
11. Connes A. Geometry from the spectral point of view Lett. Math. Phys. 34 1995 203-238
12. Connes A. Moscovici H. The local index formula in noncommutative geometry GAFA 5 1995 174-243
13. Dixmier J. Existence de traces non-normales C.R. Acad. Sci. Paris A-B 262 1966 A1107-A1108
14. J. Dixmier, Von Neumann Algebras, Vol. 27, North-Holland Mathematical Library, Amsterdam, 1981 [translation of: Les algebres d'opératurs dans l'espace hilbertien (algébres de Von Neumann), 1969]
15. Dodds P.G. Dodds T.K. de Pagter B. Fully symmetric operator spaces Integral Equations Operator Theory 15 6 1992 942-972
16. Dodds P.G. Dodds T.K. de Pagter B. Noncommutative Köthe duality Trans. Amer. Math. Soc. 339 2 1993 717-750
17. Dwight H.B. Tables of Integrals and Other Mathematical Data 4th Edition 1961 Macmillan New York
18. Fack T. private communication.
19. Fack T. Kosaki H. Generalised s-numbers of τ-measurable operators Pacific J. Math. 123 1986 269 -300
20. M. Farber, S. Weinberger, On the zero in the spectrum conjecture, Annals of Math. 154 2001 139-154
21. M. Gromov, Large Riemannian manifolds, in: K. Shiohama, T. Sakai, T. Sunada (Eds.), Curvature and Topology of Riemannian Manifolds, Lecture Notes in Mathematics, Vol 1201, 1986, pp. 108-121
22. J. Lott The zero-in-the-spectrum question, L'Enseignment Mathematique 42 1996 341-376
23. Gracia-Bondia J.M. Varilly J.C. Figueroa H. Elements of Noncommutative Geometry 2001 Birkhauser Boston
24. Kasparov G.G. The operator K-functor and extensions of C*-algebras Izv. Akad. Nauk. SSSR Ser. Mat. 44 1980 571-636
25. Loday J.-L. Cyclic Homology 2nd Edition 1998 Springer Berlin
26. Mathai V. Spectral flow, eta invariants and von Neumann algebras J. Funct. Anal. 109 1992 442-456
27. Prinzis R. Traces Residuelles et Asymptotique du Spectre des Opérateurs Pseudo-Differentiels Thèse, Université de Lyon, unpublished.
28. Sukochev F.A. Operator estimates for Fredholm modules Canad. J. Math. 52 4 2000 849-896