Schäffer's matrix inequality: the exact asymptotic constant

Samy Houache, Oleg Szehr, Rachid Zarouf

Let $S_n$ denote the smallest constant such that \[ |\det T|\|T^{-1}\| \leq S_n \|T\|^{n-1} \] for every invertible operator $T$ on every $n$-dimensional complex Banach space. In H…