DR. IMAGIRI STANLEY KATHURIMA

Citation:

Kathurima I. "Putnam-Fuglede theorem for n-Power normal and w-hyponormal operators, ." Pioneer jnl of mathematics and mathematical sciences. 2014.

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.

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.