Another consequence of Tanahashi's argument on best possibility of the grand Furuta inequality (Q1935621)

The authors show that the argument of the main result of \textit{K. Tanahashi} [Proc. Am. Math. Soc. 128, No. 2, 511--519 (2000; Zbl 0943.47016)] on the best possibility of the grand Furuta inequality has an additional consequence. In fact, they show that, under certain conditions on the parameters \(p, r, s, t, \alpha\), there exist operators \(A\) and \(B\) on \(\mathbb{R}^2\), \(0<B \leq A\), that do not satisfy the inequality \[ \{A^{r/2}(A^{-t/2}B^pA^{-t/2})^sA^{r/2}\}^{(1-t+r)/((p-t)s+r)}\leq A^{1-t+r}. \]