On norm inequalities related to the geometric mean

نویسندگان

چکیده

Let Ai and Bi be positive definite matrices for all i=1,…,m. It is shown that|||∑i=1m(Ai2♯Bi2)r|||≤|||((∑i=1mAi)rp2(∑i=1mBi)rp(∑i=1mAi)rp2)1p|||, unitarily invariant norms, where p>0 r≥1 such that rp≥1. This gives an affirmative answer to a conjecture posed by Dinh, Ahsani Tam. The preceding inequality directly leads recent result of Audenaert in 2015.

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ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2023

ISSN: ['1873-1856', '0024-3795']

DOI: https://doi.org/10.1016/j.laa.2023.04.012