  We prove pathwise uniqueness for an abstract stochastic reaction-diffusion
equation in Banach spaces. The drift contains a bounded H\"{o}lder term; in
spite of this, due to the space-time white noise it is possible to prove
pathwise uniqueness. The proof is based on a detailed analysis of the
associated Kolmogorov equation. The model includes examples not covered by the
previous works based on Hilbert spaces or concrete SPDEs.
