Generalized intertwining linear operators with isometries

Generalized intertwining linear operators with isometries

In this paper,we show that for an isometry on a Banach space the analytic spectral subspacecoincides with the algebraic spectral subspace. Using this result, we have the following result. Let $T$ be a bounded linear operator with property $(\delta)$ on a Banach space $X$. And let $S$ be an isometry on a Banach space $Y$. Then every generalized intertwining linear operator $\theta: X \to Y$for $(S,T)$ is continuous if and only if the pair $(S,T)$ has no critical eigenvalue.