Interpolating inequalities related to a recent result of Audenaert

Extensions of interpolation between the arithmetic-geometric mean inequality for matrices

“…In this section, using some ideas of [ 6 , 15 ], we extend the Audenaert results for the operator norm.…”

“…In this section, applying some ideas of [ 6 ], we generalize some interpolations for an arbitrary unitarily invariant norm.…”

“…For further information as regards the Cauchy-Schwarz inequality, see [ 3 – 5 ] and the references therein. Recently, Kittaneh et al [ 6 ] extended inequality ( 1 ) to the form where and . Audenaert [ 7 ] proved that, for all and all , we have In [ 8 ], the authors generalized inequality ( 3 ) for all and all to the form Inequality ( 4 ) interpolates between the arithmetic-geometric mean inequality.…”

“…Audenaert [ 7 ] proved that, for all and all , we have In [ 8 ], the authors generalized inequality ( 3 ) for all and all to the form Inequality ( 4 ) interpolates between the arithmetic-geometric mean inequality. In [ 6 ], the authors showed a refinement of inequality ( 4 ) for the Hilbert-Schmidt norm as follows: in which , and . The Young inequality for every unitarily invariant norm states that , where A , B are positive definite matrices and (see [ 9 ] and also [ 10 , 11 ]).…”