# DR. IMAGIRI STANLEY KATHURIMA

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

Email: imagiri@uonbi.ac.ke

Email: imagiri@uonbi.ac.ke

- Citation:
- Kathurima I. "Berger-Shaw inequality for n-Power quasinormal and w-hyponormal operators, ." Far East Jnr of Appld. Maths.. 2014.

Every reducible operator can be decomposed into normal and completely non-normal operators.

Unfortunately, there are several non normal operators which are irreducible. However, every operator

whose self-commutator is bounded, is reducible. Berger-Shaw inequality implies boundedness

of the trace of the self-commutator for hyponormal operators. In this paper, the Berger-Shaw

inequality is studied for n-Power normal, n-power quasinormal and w-hyponormal operators.

Every reducible operator can be decomposed into normal and completely non-normal operators.

Unfortunately, there are several non normal operators which are irreducible. However, every operator

whose self-commutator is bounded, is reducible. Berger-Shaw inequality implies boundedness

of the trace of the self-commutator for hyponormal operators. In this paper, the Berger-Shaw

inequality is studied for n-Power normal, n-power quasinormal and w-hyponormal operators.