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Reference for invariance of essential spectrum under relatively compact perturbations

As an answer to this question (which I spent quite a while longer looking for) I found the following reference: http://evm.ivic.gob.ve/libropaiena.pdf, a book written by Pietro Aiena. This book is wo …
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Reference for invariance of essential spectrum under relatively compact perturbations

I'm looking for a proof of the following statement: Let $X$ be a Banach space and $T$ be a closed map on $X$. For any relatively compact map $A$ the essential spectrum of $T$ and $T+A$ are the same. …
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