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We consider a stochastic evolution equation in a 2-smooth Banach space with adensely and continuously embedded Hilbert subspace. We prove that underH\"ormander's bracket condition, the image measure of the solution law underany finite-rank bounded linear operator is absolutely continuous with respectto the Lebesgue measure. To obtain this result, we apply methods of theMalliavin calculus.

A version of H\"ormander's theorem in 2-smooth Banach spaces