Abstract
In this paper, we derive an interesting result that the mixed-type reverse order laws hold if and only if the bounded linear operator products
is invariant, where
is taken, for instance, as
,
,
,
,
as well as
. Moreover, the invariance property of
is related to the reverse order law
, and we point out that such an invariance property occurs if and only if
and
are left or
and
are right invertible operators, or
is left and
is right invertible operator, where
,
and
are nonzero regular operators.
Acknowledgements
The authors would like to thank the referees for their helpful comments and suggestions.
Notes
No potential conflict of interest was reported by the authors.