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Let $A,B$ be Hermitian matrices so that $0 \le A,B < I$ and also $(1-\varepsilon)(I-B)\le I - A \le (1+\varepsilon)(I-B)$. For every $t \in \mathbb{N}$, consider the matrix $A_{t} = \sum_{i=0}^{t}...

Let $A,B$ be two $n\times n$ matrices. Find a lower bound of the $p$-th Schatten norm $\|(A-B)(A-B)^\ast\|_{S_{p/2}}^{1/2}$ in terms of Schatten norm of $\|(AA^*+BB^*)\|_{S_q}$ for any relation ...