Abstract
We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.
References
[1] A. Abdessemed and E. B. Davies, Some commutator estimates in the Schatten classes, J. London Math. Soc. (2), 41, 1989, 299-308 10.1112/jlms/s2-39.2.299Search in Google Scholar
[2] T. Furuta, An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality, Proc. Amer. Math. Soc., 81, 1981, 240–242 10.1090/S0002-9939-1981-0593465-4Search in Google Scholar
[3] D. Hadwin and E. Nordgren, Extensions of the Berger-Shaw theorem, Proc. Amer. Math. Soc., 102, 1988, 517–525 10.1090/S0002-9939-1988-0928971-XSearch in Google Scholar
[4] E. Kissin, D. Potapov, V. Shulman and F. Sukochev, Operator smoothness in Schatten norms for functions of several variables: Lipschitz conditions, differentiability and unbounded derivations, Proc. London Math. Soc. (4), 105, 2012, 661–702 10.1112/plms/pds014Search in Google Scholar
[5] F. Kittaneh, On generalized Fuglede-Putnam theorems of Hilbert-Schmidt type, Proc. Amer. Math. Soc., 88, 1983, 293–298 10.1090/S0002-9939-1983-0695261-8Search in Google Scholar
[6] F. Kittaneh, On Lipschitz functions of normal operators, Proc. Amer. Math. Soc., 94, 1985, 416–418 10.1090/S0002-9939-1985-0787884-4Search in Google Scholar
[7] T. Nakazi, Complete spectral area estimates and self-commutators, Michigan Math. J., 35, 1988, 435–441 10.1307/mmj/1029003824Search in Google Scholar
[8] V. Shulman, Some remarks on the Fuglede-Weiss theorem, Bull. London Math. Soc. (4), 28, 1996, 385-392 10.1112/blms/28.4.385Search in Google Scholar
[9] V. Shulman and L. Turowska, Operator Synthesis II. Individual synthesis and linear operator equations, J. für die reine und angewandte Math. (590), 2006, 2006, 143–187 10.1515/CRELLE.2006.007Search in Google Scholar
[10] D. Voiculescu, Some extensions of quasitriangularity, Rev. Roumaine Math. Pures Appl., 18, 1973, 1303–1320 Search in Google Scholar
[11] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators, J. Operator Theory, 2, 1979, 3–37 Search in Google Scholar
[12] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators II, J. Operator Theory, 5, 1981, 77–100 Search in Google Scholar
[13] D. Voiculescu, A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Szeged), 42, 1980, 195–199 Search in Google Scholar
[14] D. Voiculescu, Remarks on Hilbert-Schmidt perturbations of almost normal operators, Topics in Modern Operator Theory; Operator Theory: Advances and Applications-Birkhäuser, 2, 1981, 311–318 10.1007/978-3-0348-5456-6_20Search in Google Scholar
[15] D. Voiculescu, Almost Normal Operators mod Hilbert-Schmidt and the K-theory of the Algebras EΛ(Ω), arXiv:1112.4930v2 Search in Google Scholar
[16] D. Voiculescu, Hilbert space operators modulo normed ideals, Proc. Int. Congress Math., 1983, 1041–1047 Search in Google Scholar
[17] G. Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. math. Soc., 83, 1981, 113–118 10.1090/S0002-9939-1981-0619994-2Search in Google Scholar
[18] G. Weiss, Fuglede’s commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators. II, J. Operator Theory, 5, 1981, 3–16 Search in Google Scholar
© 2016 Vasile Lauric
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
