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(Last updated: September 18, 2014)

Publications

2014

Kathurima, I.  2014.  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.
Kathurima, I.  2014.  Infinite-Power normal and Infinite-Power quasinormal operators, . Pioneer jnl of mathematics and mathematical sciences,. Abstract

In this paper, infinite-Power normal and infinite-Power quasinormal operators are introduced. Amongst
other results, it is proved that, infinite-Power normal operators have translation invariant property
and that, if any operator and its adjoint happens to be n-Power quasinormal, then such an
operator becomes normal
Kathurima, I.  2014.  Berger-Shaw inequality for n-Power quasinormal and w-hyponormal operators, . Far East Jnr of Appld. Maths.. Abstract

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.
Kathurima, I.  2014.   Putnam’s inequality for n-Power normal, n-Power quasinormal and w-hyponormal operators, . Pioneer jnl of mathematics and mathematical sciences. Abstract

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. Putnam’s inequality implies boundedness
of the self-commutator for hyponormal operators. In this paper, the Putnam’s inequality is
studied for n-Power normal, n-power quasinormal and w-hyponormal operators.
Kathurima, I.  2014.  Putnam-Fuglede theorem for n-Power quasinormal and w-hyponormal operators. Far East Jnr of Appld. Maths..
Kathurima, I.  2014.  An Interplay Between n-Power quasinormal and w-Hyponormal operators,. Far East Jnr of Appld. Maths.. 88 Abstract

In this monograph, via Aluthge transformations, it is proved that every n-Power normal operator
is normaloid and through paranormality, w-hyponormal operators are shown to be indepedent
from n-Power normal, hence from n-Power quasinormal operators. Nevertheless, an attempt to
throw more materials- rather than the class of normal operators-, in the intersection of these
non-normal classes is presented.

2013

and S.K Imagiri, KPJMGP.  2013.  Normality of the products of nth-Aluthge transforms of w-Hyponormal operators.. Far East Jnr. Of Maths.
and 1 S.K Imagiri, KPJMGP.  2013.  Restrictions on the Powers of Generalized Aluthge Transforms of w-Hyponormal Operators. Far East Jnl of Maths .

2012

and S.K Imagiri, KPJMGP.  2012.  Normality of the products n-Power quasi normal operators, . Far East Jnr. of Maths..

2011

and S.K Imagiri, KPJMGP.  2011.  On the nth-Aluthge transforms of w-Hyponormal operators. Far East Jnr. Of Maths.

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