An operator-coefficients free Poincaré inequality

Abstract

We prove the following operator-coefficients free Poincaré inequality: $$|f(X)-E[f(X)]{|}_2\le 2|X{|}_2\Vert {\hat{\partial }}_{X:B}[f(X)]{\Vert }_{\pi },f(X)\in \mathrm{dom}({\hat{\partial }}_{X:B}),$$ where $\Vert \cdot {\Vert }_{\pi }$ is the projective tensor norm.

4 pages; any comments are welcome