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arXiv · 1501.01897

Essential Spectra of Induced Operators on Subspaces and Quotients

D. C. Moore
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Abstract

Let $X$ be a complex Banach space and let $T$ be a bounded linear operator on $X$. For any closed $T$-invariant subspace $F$ of $X$, $T$ induces operators $T_{|F}:F \longrightarrow F$ and $T/F:X/F\longrightarrow X/F$. In this note, we give a simple proof of the fact that the essential spectra of $T_{|F}$ and $T/F$ are always contained in the polynomial hull of the essential spectrum of $T$.

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D. C. Moore. 2015-01-08. Essential Spectra of Induced Operators on Subspaces and Quotients. https://arxiv.org/abs/1501.01897

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