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Some notable results on approximate pseudospectrum

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The concept of approximate pseudospectrum is studied in this note. We first prove that any open ball of an element in the approximate spectrum is a subset of approximate pseudospectrum. We also have derived some results related to mapping theorem of approximate pseudospectrum. Examples are given to throw light on the established outcomes.
Title: Some notable results on approximate pseudospectrum
Description:
The concept of approximate pseudospectrum is studied in this note.
We first prove that any open ball of an element in the approximate spectrum is a subset of approximate pseudospectrum.
We also have derived some results related to mapping theorem of approximate pseudospectrum.
Examples are given to throw light on the established outcomes.

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