Remarks on Fuglede-Putnam theorem for normal operators modulo the Hilbert-Schmidt class

Vasile Lauric
2014 International Mathematical Forum  
In a recent note, we proved a Fuglede-Putnam commutativity theorem for almost normal operators with finite modulus of C 2 -quasitriangularity modulo the Hilbert-Schmidt class. In this note we show how our proof can be adjusted to the case of normal operators to obtain an optimal norm estimate obtained by G. Weiss. The result is also reviewed in the case of almost normal operators with zero modulus of C 2 -quasitriangularity for the operator and its adjoint and an example is provided.
more » ... rovided. Mathematics Subject Classification: 47B20
doi:10.12988/imf.2014.47141 fatcat:7g3kuj56ibcp3agzxffn2ugno4