Toeplitz and hankel operators and dixmier traces on the unit ball of ℂn

Proceedings of the American Mathematical Society

Volumn 137, Issue 11, 2009, Pages 3669-3678

  Engliš, Miroslav ^a,b   Guo, Kunyu ^c   Zhang, Genkai ^d  

^a INSTITUTE OF MATHEMATICS   (Czech Republic)

^b SILESIAN UNIVERSITY IN OPAVA   (Czech Republic)

^c FUDAN UNIVERSITY   (China)

^d CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Boundary CR operators; Dixmier trace; Hankel operators; Invariant Banach spaces; Macaev classes; Pseudo differential operators; Pseudo Toeplitz operators; Schatten von Neumann classes; Toeplitz operators; Trace

Indexed keywords

EID: 77950851522     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-09-09331-9     Document Type: Article

References (19)

1. J. Arazy, S. D. Fisher, and J. Peetre, Hankel operators on weighted Bergman spaces, Amer. J. Math. 110 (1988), no. 6, 989-1053. MR970119 (90a:47067)
2. J. Arazy, S. D. Fisher, S. Janson, and J. Peetre, An identity for reproducing kernels in a planar domain and Hilbert-Schmidt Hankel operators, J.Reine Angew. Math. 406 (1990), 179-199. MR1048240 (91b:47050)
3. -, Membership of Hankel operators on the ball in unitary ideals, J. London Math. Soc. (2) 43 (1991), no. 3, 485-508. MR1113389 (93c:47030)
4. n, J. Funct. Anal. 203 (2003), no. 2, 305-320. MR2003350 (2004g:58036)
5. M. Feldman and R. Rochberg, Singular value estimates for commutators and Hankel operators on the unit ball and the Heisenberg group, Analysis and partial differential equations, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 121-159. MR1044786 (91e:47024)
6. V. Guillemin, Toeplitz operators in n dimensions, Integral Equations Operator Theory 7 (1984), no. 2, 145-205. MR750217 (86i:58130)
7. A. Connes, The action functional in noncommutative geometry, Comm. Math. Phys. 117 (1988), no. 4, 673-683. MR953826 (91b:58246)
8. A. Connes, Noncommutative geometry, Academic Press Inc., San Diego, CA, 1994. MR1303779 (95j:46063)
9. J. W. Helton and R. E. Howe, Traces of commutators of integral operators, Acta Math. 135 (1975), no. 3-4, 271-305. MR0438188 (55:11106)
10. R. Howe, Quantum mechanics and partial differential equations, J. Funct. Anal. 38 (1980), no. 2, 188-254. MR587908 (83b:35166)
11. S. Janson, J. Peetre, and R. Rochberg, Hankel forms and the Fock space, Rev.Mat. Iberoamericana 3 (1987), no. 1, 61-138. MR1008445 (91a:47029)
12. S. Janson, H. Upmeier, and R. Wallsten, Schatten-norm identities for Hankel operators, J. Funct. Anal. 119 (1994), no. 1, 210-216. MR1255278 (95a:47021)
13. J. Peetre, On the S-norm of a Hankel form, Rev. Mat. Iberoamericana 8 (1992), no. 1, 121-130. MR1178451 (93f:47027)
14. V. V. Peller, Hankel operators and their applications, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003. MR1949210 (2004e:47040)
15. R. Ponge, Noncommutative residue invariants for CR and contact manifolds, J.ReineAngew. Math. 614 (2008), 117-151. MR2376284 (2008j:58039)
16. R. Rochberg, Trace ideal criteria for Hankel operators and commutators, Indiana Univ. Math. J. 31 (1982), no. 6, 913-925. MR674875 (84d:47036)
17. n, Springer-Verlag, New York-Berlin, 1980. MR601594 (82i:32002)
18. E. M. Stein, Harmonic analysis: Real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993, with the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III. MR1232192 (95c:42002)
19. K. H. Zhu, Schatten class Hankel operators on the Bergman space of the unit ball, Amer.J. Math. 113 (1991), no. 1, 147-167. MR1087805 (91m:47036)i