The spectral shift function and spectral flow

Communications in Mathematical Physics

Volumn 276, Issue 1, 2007, Pages 51-91

  Azamov, N A ^a   Carey, A L ^b   Sukochev, F A ^a  

^a FLINDERS UNIVERSITY   (Australia)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848835723     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0329-9     Document Type: Article

References (37)

1. Asplund E. and Bungart L. (1966). A First Course in Integration. Holt, Rinehart and Winston, New York
2. Atiyah M., Patodi V. and Singer I.M. (1976). Spectral Asymmetry and Riemannian Geometry. III. Math. Proc. Camb. Phil. Soc. 79: 71-99
3. Azamov, N.A., Carey, A.L., Dodds, P.G., Sukochev, F.A.: Operator integrals, spectral shift and spectral flow. to appear in Canad. J. Math, available at http://arxiv.org/list/math/0703442, 2007
4. Azamov N.A., Dodds P.G. and Sukochev F.A. (2006). The Krein spectral shift function in semi-finite von Neumann algebras. Integral Equations Operator Theory 55: 347-362
5. Benameur, M.-T., Carey, A.L., Phillips, J., Rennie, A., Sukochev, F.A., Wojciechowski, K.P.: An analytic approach to spectral flow in von Neumann algebras. In: Analysis, geometry and topology of elliptic operators, Hackensack, NJ: World Sci. Publ., 2006, pp. 297-352
6. Birman M.Sh. and Pushnitski A.B. (1998). Spectral shift function, amazing and multifaceted. Dedicated to the memory of Mark Grigorievich Krein (1907-1989). Integral Equations Operator Theory 30: 191-199
7. Birman M.Sh. and Solomyak M.Z. (1975). Remarks on the spectral shift function. J. Soviet Math. 3: 408-419
8. Birman, M.Sh., Solomyak, M.Z.: Double Stieltjes operator integrals. I. In: Problems of Mathematical Physics, No. 1, Spectral Theory and Wave Processes, Leningrad: Izdat. Leningrad. Univ., 1966, pp. 33-67 (Russian)
9. Birman, M.Sh., Solomyak, M.Z.: Double Stieltjes operator integrals. II. In: Problems of Mathematical Physics, No. 2, Spectral Theory, Diffraction Problems, Leningrad: Izdat. Leningrad. Univ., 1967, pp. 26-60 (Russian)
10. Birman, M.Sh., Solomyak, M.Z.: Double Stieltjes operator integrals. III, Leningrad: Izdat. Leningrad Univ., 1973, pp. 27-53 (Russian)
11. Birman M.Sh. and Yafaev D.R. (1992). The spectral shift function, the work of M. G. Krein and its further development. Algebra i Analiz 4: 833-870
12. Booß-Bavnbek B., Lesch M. and Phillips J. (2005). Unbounded Fredholm operators and spectral flow. Canad. J. Math. 57: 225-250
13. Bratteli O. and Robinson D. (1979). Operator Algebras and Quantum Statistical Mechanics I. Springer-Verlag, Berlin-Heidelberg-Newyork
14. Carey A.L., Hannabuss K.C., Mathai V. and McCann P. (1998). The quantum hall effect on the hyperbolic plane. Commun. Math. Phys 190: 629-673
15. Carey A.L. and Phillips J. (1998). Unbounded Fredholm modules and spectral flow. Canad. J. Math. 50: 673-718
16. Carey A.L. and Phillips J. (2004). Spectral flow in Fredholm modules, eta invariants and the JLO cocycle. K-Theory 31: 135-194
17. Carey A.L., Phillips J., Rennie A. and Sukochev F.A. (2006). The local index formula in semifi- nite von Neumann algebras I: spectral flow. Adv. in Math. 202: 451-516
18. Carey A.L., Phillips J., Rennie A. and Sukochev F.A. (2006). The local index formula in semifi- nite von Neumann algebras II: even case. Adv. in Math. 202: 517-554
19. Connes A. (1994). Noncommutative Geometry. Academic Press, San Diego
20. Connes A. and Moscovici H. (1995). The local index formula in noncommutative geometry. GAFA 5: 174-243
21. Daletskiǐ Yu.L. and Kreǐn S.G. (1956). Integration and differentiation of functions of Hermitian operators and applications to the theory of perturbations. Voronež. Gos. Univ., Trudy Sem. Funkcional. Anal. 1: 81-105 (Russian)
22. Fack T. and Kosaki H. (1986). Generalised s-numbers of τ-measurable operators. Pacific J. Math. 123: 269-300
23. Gelfand I.M. and Shilov G.E. (1964). Generalized functions, Vol. 1. Academic Press, New York
24. Getzler E. (1993). The odd Chern character in cyclic homology and spectral flow. Topology 32: 489-507
25. Jacobs K. (1978). Measure and integral. Academic Press, New York-San Francisco-London
26. Kreǐn, M.G.: Some new studies in the theory of perturbations of self-adjoint operators. (Russian) First Math. Summer School (Kanev, 1963), Part I, Kiev: Naukova Dumka, 1964, pp. 103.187;
27. English transl. in M.G. Kreǐn: Topics in differential and integral equations and operator theory, Basel: Birkhäuser, 1983, pp. 107-172
28. de Pagter B. and Sukochev F.A. (2004). Differentiation of operator functions in noncommutative Lp-spaces. J. Funct. Anal. 212: 28-75
29. Peller, V.V.: Multiple operator integrals and higher operator derivatives. http://arxiv.org/list/math.SP/ 0505555, 2005
30. Phillips J. and Raeburn I. (1994). An index theorem for Toeplitz operators with noncommutative symbol space. J. Funct. Anal. 120: 239-263
31. Phillips J. (1996). Self-adjoint Fredholm operators and spectral flow. Canad. Math. Bull. 39: 460-467
32. Phillips J. (1997). Spectral flow in type I and type II factors - a new approach. Fields Inst. Comm. 17: 137-153
33. Simon, B.: Trace ideals and their applications. London Math. Society Lecture Note Series 35, Cambridge-London: Cambridge University Press, 1979
34. Simon B. (1998). Spectral averaging and the Krein spectral shift. Proc. Amer. Math. Soc. 126: 1409-1413
35. Takesaki M. (2002). Theory of Operator Algebras. Vol. I. Springer-Verlag, Berlin Heidelberg-Newyork
36. Wahl, C.: Spectral flow as winding number and integral formulas. http://arxiv.org/list/math/0703287, 2007
37. Wahl, C.: A new topology on the space of unbounded selfadjoint operators and the spectral flow. http://arxiv.org/list/math/0607783, 2006