Putnam-Fuglede Theorem For N-Power Normal And W-hyponormal Operators,

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.