2000 character limit reached
On the conjecture of the norm Schwarz inequality (1606.04231v1)
Published 14 Jun 2016 in math.FA
Abstract: For any positive invertible matrix $A$ and any normal matrix $B$ in $M_{n}({\Bbb C})$, we investigate whether the inequality $ ||A\sharp (B{*}A{-1}B)||\geq ||B|| $ is true or not, where $\sharp$ denotes the geometric mean and $||\cdot||$ denotes the operator norm. We will solve this problem negatively. The related topics are also discussed.