Abstract
A complex number ? is an extended eigenvalue of an operator A if there is a nonzero operator B such that = ?BA. In this case, B is said to be an eigenoperator. This research paper is devoted to the investigation of some results of extended eigenvalues for a closed linear operator on a complex Banach space. The obtained results are explored in terms two cases bounded, and closed eigenoperators. In addition, the notion of extended eigenvalues for a 2 ? 2 upper triangular operator matrix is introduced and some of its properties are displayed.
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