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Volume 9, Issue 1 (2017) , Pages [1] - [50]
A FUGLEDE-PUTNAM TYPE THEOREM FOR ALMOST 
[1] Vasile Lauric, A Fuglede-Putnam theorem modulo the Hilbert-Schmidt class for almost normal operators with finite modulus of Hilbert-Schmidt quasi-triangularity, Concr. Oper. 3 (2016), 8-14.
[2] Dan V. Voiculescu, Some results on norm-ideal perturbations of Hilbert space operators II, J. Operator Theory 5 (1981), 77-100.
[3] Dan V. Voiculescu, Hilbert space operators modulo normed ideals, Proceedings of the International Congress of Mathematicians, August 16-24, Warszawa (1983), 1041-1047.
[4] Dan V. Voiculescu, Almost normal operators mod Hilbert-Schmidt and the K-theory of the algebras 
J. Noncommut. Geom. 8 (2014), 11231-1145.
[5] Gary Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. Math. Soc. 83 (1981), 113-118.