A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity

Vasile Lauric

Concrete Operators (2016)

  • Volume: 3, Issue: 1, page 8-14
  • ISSN: 2299-3282

Abstract

top
We extend the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to almost normal operators with finite Hilbert-Schmidt modulus of quasi-triangularity.

How to cite

top

Vasile 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. [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. [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. [3] D. Hadwin and E. Nordgren, Extensions of the Berger-Shaw theorem, Proc. Amer. Math. Soc., 102, 1988, 517–525  Zbl0659.47026
  4. [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. [5] F. Kittaneh, On generalized Fuglede-Putnam theorems of Hilbert-Schmidt type, Proc. Amer. Math. Soc., 88, 1983, 293–298  Zbl0521.47014
  6. [6] F. Kittaneh, On Lipschitz functions of normal operators, Proc. Amer. Math. Soc., 94, 1985, 416–418  Zbl0549.47006
  7. [7] T. Nakazi, Complete spectral area estimates and self-commutators, Michigan Math. J., 35, 1988, 435–441  Zbl0675.47013
  8. [8] V. Shulman, Some remarks on the Fuglede-Weiss theorem, Bull. London Math. Soc. (4), 28, 1996, 385-392  Zbl0892.47007
  9. [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. [10] D. Voiculescu, Some extensions of quasitriangularity, Rev. Roumaine Math. Pures Appl., 18, 1973, 1303–1320  Zbl0273.47009
  11. [11] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators, J. Operator Theory, 2, 1979, 3–37  Zbl0446.47003
  12. [12] D. Voiculescu, Some results on norm-ideal perturbation of Hilbert space operators II, J. Operator Theory, 5, 1981, 77–100  Zbl0483.46036
  13. [13] D. Voiculescu, A note on quasitriangularity and trace-class self-commutators, Acta Sci. Math. (Szeged), 42, 1980, 195–199  Zbl0441.47022
  14. [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. [15] D. Voiculescu, Almost Normal Operators mod Hilbert-Schmidt and the K-theory of the Algebras EΛ(Ω), arXiv:1112.4930v2  Zbl1325.46074
  16. [16] D. Voiculescu, Hilbert space operators modulo normed ideals, Proc. Int. Congress Math., 1983, 1041–1047  
  17. [17] G. Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. math. Soc., 83, 1981, 113–118  Zbl0478.47004
  18. [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 ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.