LINEAR OPERATORS FOR WHICH TT^D IS NORMAL
Abstract
In this paper we introduce and analyze a new class of generalized normal
operators, namely skew D-quasi-normal operators, associated with a Drazin in-
vertible operator using its Drazin inverse. After establishing the basic properties
of such operators, we give examples and discuss how this class of operators is
distinct from several other operator classes. For S T 2 Mn(C), we investigate
a necessary and sucient condition for the skew D-quasi-normality of ST and
TS. Also, we deduce a result relating the factors in a polar decomposition
of S to the skew D-quasi-normality of ST and TS. Moreover, we generalize
Fuglede-Putnam commutativity theorem for skew D-quasi-normal matrices.
operators, namely skew D-quasi-normal operators, associated with a Drazin in-
vertible operator using its Drazin inverse. After establishing the basic properties
of such operators, we give examples and discuss how this class of operators is
distinct from several other operator classes. For S T 2 Mn(C), we investigate
a necessary and sucient condition for the skew D-quasi-normality of ST and
TS. Also, we deduce a result relating the factors in a polar decomposition
of S to the skew D-quasi-normality of ST and TS. Moreover, we generalize
Fuglede-Putnam commutativity theorem for skew D-quasi-normal matrices.
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