An invariance property of operator products related to the mixed-type reverse order laws
Xiaoji Liu, Shiqin Fu, Yaoming Yu · Linear and Multilinear Algebra · 2015
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.