Spectral flow and Dixmier traces

Advances in Mathematics

Volumn 173, Issue 1, 2003, Pages 68-113

  Carey, Alan ^a   Phillips, John ^b   Sukochev, Fyodor ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF VICTORIA   (Canada)

^c FLINDERS UNIVERSITY   (Australia)

Author keywords

Dixmier trace; Spectral flow; Zeta function; (p, ) summable Fredholm module

Indexed keywords

EID: 0037440272     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0001-8708(02)00015-4     Document Type: Article

References (29)

1. M. Abramowitz, I.A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, U.S. Govt. Print. Off, Washington, 1964.
2. M.S. Birman, L.S. Koplienko, M.Z. Solomyak, Estimates for the spectrum of the difference between fractional powers of two selfadjoint operators, Soviet Math. 19 (3) (1975) 1-6.
3. O. Bratteli, D. Robinson, Operator Algebras and Quantum Statistical Mechanics I, Springer, New York, Heidelberg, Berlin, 1979.
4. A. Connes, H. Moscovici, The local index formula in non-commutative geometry, Geom. Funct. Anal. 5 (1995) 174-243.
5. A.L. Carey, J. Phillips, Unbounded Fredholm modules and spectral flow, Canad. J. Math. 50 (4) (1998) 673-718.
6. A.L. Carey, J. Phillips, Theta summable Fredholm modules, eta invariants and spectral flow, Preprint.
7. A.L. Carey, J. Phillips, F.A. Sukochev, On unbounded p-summable Fredholm modules, Adv. in Math. 151 (2000) 140-163.
8. A. Connes, Noncommutative differential geometry, Publ. Math. Inst. Hautes Etudes Sci. (Paris) 62 (1985) 41-144.
9. A. Connes, Cyclic cohomology of Banach algebras and characters of θ-summable Fredholm modules, K-Theory 1 (1988) 519-548.
10. A. Connes, Compact metric spaces, Fredholm modules and hyperfiniteness, Ergodic Theory Dyn. Systems 9 (1989) 207-220.
11. A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994.
12. V.I. Chilin, F.A. Sukochev, Weak convergence in non-commutative symmetric spaces, J. Operator Theory 31 (1994) 35-65.
13. J. Dixmier, Les algèbres d'opérateurs dans l'espace Hilbertien (Algèbres de von Neumann), Gauthier-Villars, Paris, 1969.
14. J. Dixmier, Existence de traces non-normales, C.R. Acad. Sci. Paris A-B 262 (1966) A1107-A1108.
15. P.G. Dodds, B. de Pagter, E.M. Semenov, F.A. Sukochev, Symmetric functionals and singular traces, Positivity 2 (1998) 47-75.
16. R.E. Edwards, Functional Analysis: Theory and Applications, Holt, Rinehart and Winston, New York, 1965.
17. T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory 7 (1982) 307-333.
18. T. Fack, H. Kosaki, Generalised s-numbers of τ-measurable operators, Pacific J. Math. 123 (1986) 269-300.
19. F.P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand Reinhold, New York, 1969.
20. I.C. Gohberg, M.G. Krein, Introduction to the Theory of Non-selfadjoint Operators, in: Translations of Mathematical Monographs, Vol. 18, Amer. Math. Soc, Providence, RI, 1969.
21. 2 Hodge theory, J. Differential Geom. 33 (1991) 263-292.
22. J.M. Gracia-Bondia, J.C. Varilly, H. Figueroa, Elements of Noncommutative Geometry, Birkhauser, Boston, 2001.
23. G.H. Hardy, Divergent Series, Clarendon, Oxford, 1949.
24. R. Kadison, J. Ringrose, Fundamentals of the Theory of Operator Algebras, Birkhauser, Boston, 1983.
25. M. Lesch, On the index of the infinitesimal generator of a flow, J. Operator Theory 26 (1991) 73-92.
26. R. Prinzis, Traces residuelles et asymptotique du Spectre d'opérateurs pseudo-differentiels, Thèse, Université de Lyon, unpublished.
27. J. Phillips, Self-adjoint Fredholm operators and spectral flow, Canad. Math. Bull. 39 (1996) 460-467.
28. J. Phillips, Spectral flow in type I and II factors - A new approach, Fields Inst. Comm. 17 (1997) 137-153.
29. J. Phillips, I. Raeburn, An index theorem for Toeplitz operators with noncommutative symbol space, J. Funct. Anal. 120 (1994) 239-263.