‎We review some significant generalizations and applications of the celebrated Douglas theorem on equivalence of factorization‎, ‎range inclusion‎, ‎and majorization of operators‎. ‎We then apply it to find a characterization ...

‎It is known that for every $t\\\\\\\\in (0,1]$ and every $k$-tuple of positive invertible operators ${\\\\\\\\Bbb A}=(A_1,\\\\\\\\ldots,A_k)$‎ , ‎the Ando--Hiai type inequality for operator power means‎
‎\\\\\\\\[ ...

‎In this paper‎, ‎we prove that if Phi‎: mathscr{A} to mathscr{B} is a bounded linear map between C^*-algebras‎, ‎then‎
begin{equation*}‎
left|sum_{k=1}^n left{|Phi(A_k)|^2+|Phi(A_k^*)|^2right}right|leq 2 |Phi|^2 ...