Extended eigenvalues of 2 x 2 block operator matrices

In this work, the notion of extended eigenvalues of a 2 x 2 lower triangular operator matrix has been researched. More precisely, the relations between the extended spectrum of a 2 x 2 lower triangular operator matrix with the spectrum, the point spectrum, and the extended spectrum of its diagonal entries have been investigated. The obtained results have been supplemented by examples. In addition, some properties of the extended spectrum of 2 x 2 block operator matrices have been displayed.