ON SPECTRAL SUBSPACES OF SEMI-SHIFTS

Abstract

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 X and let S be a semi-shift on a Banach space Y. Then every linear operator θ : X → Y with Sθ = θT is necessarily continuous.

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