An operator-coefficients free Poincaré inequality

preprint2023arXivOpen access

We prove the following operator-coefficients free Poincaré inequality: $|f(X)-E[f(X)]|_{2}\leq2|X|_{2}\|\widehat{\partial}_{X:B}[f(X)]\|_π, \quad f(X) \in \mathrm{dom}(\widehat{\partial}_{X:B}),$ where $\|\cdot\|_π$ is the projective tensor norm.

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An operator-coefficients free Poincaré inequality

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