# DR. IMAGIRI STANLEY KATHURIMA

## BSc, MSc, PhD, (Nairobi) Applied Mathematics

Email: imagiri@uonbi.ac.ke

Email: imagiri@uonbi.ac.ke

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

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.