Matrix inequalities related to Hölder inequality
The main results of this paper are Hölder-type matrix inequalities for sums and products of matrices that generalize a Hölder-type matrix inequality proved by \textit{T. Ando} and \textit{F. Hiai} [Math. Inequal. Appl. 1, No. 1, 1--30 (1998; Zbl 0897.15008)]. One of these results is the following theorem: Let \(2 \leqslant p,q \leqslant \infty\) und \(r > 1\) with \(1/p+1/q=1-1/r\). Then for any \({A_i},{B_i} \in {M_n}({\mathbb C})\) and \({\alpha _i} \in [0,1]\) \((i = 1,2,\dots,m)\) with \(\sum_{i = 1}^m {{\alpha _i} = 1}\), we have \(\left| \sum_{i = 1}^m \alpha _i^{1/r} B_i A_i\right| \leqslant \left(\sum_{i = 1}^m \left| A_i \right|^p \right)^{1/p}\) whenever \(\sum_{i = 1}^m \left| B_i^* \right|^q\).
scientific article; zbMATH DE number 6147465
scientific article