Putnam-Fuglede theorem for n-Power normal and w-hyponormal operators, .
Pioneer jnl of mathematics and mathematical sciences. Abstract
Reducibility implies direct sum decompositions of Hilbert space operators and any pair of operators
which satisfy the Putnam-Fuglede theorem is reducible. In this presentation, the familiar
Putnam-Fuglede theorem is firstly investigated for n-Power normal operators. Then, it’s assymetric
version is studied for n-Power normal and w-hyponormal operators. As a consequence,
more conditions implying normality, or even similarlity between these two operator classes, are
deduced via this theorem.