4 problems

Let $\{A_n\}_n$ and $\{B_n\}_n$ be Hermitian positive definite GLT matrix-sequences with matrix-valued GLT symbols … Assume…

Generalized geometric-mean conjecture. If $0\leq t\leq1$, $p\geq1$, and either $r,s\geq1$ or $r,s\leq0$, then

Monotonicity conjecture. The function

Let $H$ and $K$ be Hermitian matrices, let $I$ denote the identity matrix, and for positive definite matrices define the weighted geometric mean by … The preceding argument establi…