Measurable operators and the asymptotics of heat kernels and zeta functions

Journal of Functional Analysis

Volumn 262, Issue 10, 2012, Pages 4582-4599

  Carey, Alan ^a   Sukochev, Fedor ^b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Ces ro operator; Dixmier traces; Generalized limits; Heat kernels; Measurable elements

Indexed keywords

EID: 84858797777     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2012.03.008     Document Type: Article

References (27)

1. Allan A., Barany M., Strichartz R.S. Spectral operators on the Sierpinski gasket, I. Complex Var. Elliptic Equ. 2009, 54:521-543.
2. Benameur M., Fack T. Type II noncommutative geometry. I. Dixmier trace in von Neumann algebras. Adv. Math. 2006, 199:29-87.
3. Carey A., Phillips J., Sukochev F. Spectral flow and Dixmier traces. Adv. Math. 2003, 173(1):68-113.
4. Carey A., Rennie A., Sedaev A., Sukochev F. The Dixmier trace and asymptotics of zeta functions. J. Funct. Anal. 2007, 249(2):253-283.
5. Carey A., Sukochev F. Dixmier traces and some applications to noncommutative geometry. Uspekhi Mat. Nauk. Russian Math. Surveys 2006, 61(6):1039-1099. (in Russian), English translation in.
6. Connes A. The action functional in non-commutative geometry. Comm. Math. Phys. 1988, 117:673-683.
7. Connes A. Noncommutative Geometry 1994, Academic Press, San Diego.
8. Derfel G., Grabner P.J., Vogl F. The zeta function of the Laplacian on certain fractals. Trans. Amer. Math. Soc. 2008, 360:881-897.
9. Dixmier J. Existence de traces non normales. C. R. Acad. Sci. Paris 1966, 262:A1107-A1108.
10. Gohberg I.C., Krein M.G. Introduction to the Theory of Non-Selfadjoint Operators. Transl. Math. Monogr. 1969, vol. 18. Amer. Math. Soc.
11. Gohberg I.C., Krein M.G. Theory and Applications of Volterra Operators on Hilbert Space. Transl. Math. Monogr. 1970, vol. 24. Amer. Math. Soc.
12. Hardy G. Divergent Series 1949, Oxford University Press, Oxford.
13. Krein S., Petunin Ju., Semenov E. Interpolation of Linear Operators. Transl. Math. Monogr. 1982, vol. 54. Nauka, Moscow, (in Russian), English translation in, Amer. Math. Soc.
14. Kalton N., Sedaev A., Sukochev F. Fully symmetric functionals on a Marcinkiewicz space are Dixmier traces. Adv. Math. 2011, 226(4):3540-3549.
15. Kigami J. Analysis on Fractals 2001, Cambridge University Press, Cambridge.
16. Lord S., Sukochev F. Measure theory in noncommutative spaces. SIGMA Symmetry Integrability Geom. Methods Appl. 2010, 6. 072, 36 pp.
17. Lord S., Sedaev A., Sukochev F. Dixmier traces as singular symmetric functionals and applications to measurable operators. J. Funct. Anal. 2005, 224(1):72-106.
18. Lindenstrauss J., Tzafriri L. Classical Banach Spaces. II. Function Spaces. Results Math. Related Areas 1979, vol. 97. Springer-Verlag, Berlin-New York.
19. Matsaev V.I. On a class of completely continuous operators. Soviet Math. Dokl. 1961, 2:972-975.
20. 1,∞. Rev. Mat. Complut. 2009, 22:209-226.
21. p spaces. J. Lond. Math. Soc. 1960, 35:161-171.
22. Sedaev A. Singular symmetric functionals and stabilizing subsets of the Marcinkiewicz space. Izv. Vyssh. Uchebn. Zaved. Mat.. Russian Math. (Iz. VUZ) 2009, 53(12):77-80. (in Russian), English translation in.
23. Sedaev A. Generalized limits and related asymptotic formulas. Mat. Zametki. Math. Notes 2009, 86(3-4):577-590. (in Russian), English translation in.
24. A. Sedaev, F. Sukochev, Connes measurability in Marcinkiewicz spaces and applications, submitted for publication.
25. B.A. Steinhurst, A. Teplyaev, Existence of a meromorphic extension of spectral zeta functions on fractals, preprint.
26. F. Sukochev, A. Usachev, D. Zanin, Generalized limits with additional invariance properties and their applications to noncommutative geometry, submitted for publication.
27. Sukochev F., Zanin D. ζ-function and heat kernel formulae. J. Funct. Anal. 2011, 260(8):2451-2482.