Abstract
In this note we give conditions for continuity of spectrum, approximative point spectrum and defect spectrum on the set <TEX>$\{T\}+\mathcal{K}(X)$</TEX>, where <TEX>$T{\in}\mathcal{B}(X)$</TEX> and <TEX>$\mathcal{K}(X)$</TEX> is the set of compact operators.
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