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We show the pathwise uniqueness for stochastic partial differential equationdriven by a cylindrical $\alpha$-stable process with H\"older continuous drift,thus obtaining an infinite dimensional generalization of the result of Priola[Osaka J. Math., 2012] in the case $H=\mathbb{R}^d$. The proof is based on aninfinite dimensional Kolmogorov equation with non-local operator.

Pathwise uniqueness for a class of SPDEs driven by cylindrical $\alpha$-stable processes