ON SPECTRAL SUBSPACES OF SEMI-SHIFTS

In this paper, we show that for a semi-shift the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a decomposable operator on a Banach space ${\mathcal{X}}$ and let S be a semi-shift on a Banach space ${\mathcal{Y}}$. Then every linear operator ${\theta}:{\mathcal{X}}{\rightarrow}{\mathcal{Y}}$ with $S{\theta}={\theta}T$ is necessarily continuous.