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We obtain sequence space representations for a class of Fr\'echet spaces ofentire functions with rapid decay on horizontal strips. In particular, we showthat the projective Gelfand-Shilov spaces $\Sigma^1_\nu$ and $\Sigma^\nu_1$ areisomorphic to $\Lambda_{\infty}(n^{1/(\nu+1)})$ for $\nu > 0$.

Sequence space representations for spaces of entire functions with rapid decay on strips