A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity
Concrete Operators (2016)
- Volume: 3, Issue: 1, page 8-14
- ISSN: 2299-3282
Access Full Article
topAbstract
topHow to cite
topVasile Lauric. "A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity." Concrete Operators 3.1 (2016): 8-14. <http://eudml.org/doc/276601>.
@article{VasileLauric2016,
abstract = {We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.},
author = {Vasile Lauric},
journal = {Concrete Operators},
keywords = {Hilbert-Schmidt and trace-class operators; Almost normal operators; Almost hyponormal operators; Modulus of quasi-triangularity; almost normal operators; almost hyponormal operators; modulus of quasi-triangularity},
language = {eng},
number = {1},
pages = {8-14},
title = {A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity},
url = {http://eudml.org/doc/276601},
volume = {3},
year = {2016},
}
TY - JOUR
AU - Vasile Lauric
TI - A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity
JO - Concrete Operators
PY - 2016
VL - 3
IS - 1
SP - 8
EP - 14
AB - We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.
LA - eng
KW - Hilbert-Schmidt and trace-class operators; Almost normal operators; Almost hyponormal operators; Modulus of quasi-triangularity; almost normal operators; almost hyponormal operators; modulus of quasi-triangularity
UR - http://eudml.org/doc/276601
ER -
References
top- [1] A. Abdessemed and E. B. Davies, Some commutator estimates in the Schatten classes, J. London Math. Soc. (2), 41, 1989, 299-308 Zbl0692.47009
- [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 Zbl0458.47020
- [3] D. Hadwin and E. Nordgren, Extensions of the Berger-Shaw theorem, Proc. Amer. Math. Soc., 102, 1988, 517–525 Zbl0659.47026
- [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 Zbl1258.47022
- [5] F. Kittaneh, On generalized Fuglede-Putnam theorems of Hilbert-Schmidt type, Proc. Amer. Math. Soc., 88, 1983, 293–298 Zbl0521.47014
- [6] F. Kittaneh, On Lipschitz functions of normal operators, Proc. Amer. Math. Soc., 94, 1985, 416–418 Zbl0549.47006
- [7] T. Nakazi, Complete spectral area estimates and self-commutators, Michigan Math. J., 35, 1988, 435–441 Zbl0675.47013
- [8] V. Shulman, Some remarks on the Fuglede-Weiss theorem, Bull. London Math. Soc. (4), 28, 1996, 385-392 Zbl0892.47007
- [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 Zbl1094.47054
- [10] D. Voiculescu, Some extensions of quasitriangularity, Rev. Roumaine Math. Pures Appl., 18, 1973, 1303–1320 Zbl0273.47009
- [11] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators, J. Operator Theory, 2, 1979, 3–37 Zbl0446.47003
- [12] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators II, J. Operator Theory, 5, 1981, 77–100 Zbl0483.46036
- [13] D. Voiculescu, A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Szeged), 42, 1980, 195–199 Zbl0441.47022
- [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
- [15] D. Voiculescu, Almost Normal Operators mod Hilbert-Schmidt and the K-theory of the Algebras EΛ(Ω), arXiv:1112.4930v2 Zbl1325.46074
- [16] D. Voiculescu, Hilbert space operators modulo normed ideals, Proc. Int. Congress Math., 1983, 1041–1047
- [17] G. Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. math. Soc., 83, 1981, 113–118 Zbl0478.47004
- [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
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.