Browder S-Resolvent Equation in Quaternionic Setting

This paper is devoted to the study of the S -eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic Hilbert space. The study is based on the different properties of the Riesz projection associated with the connected part of the S -spectrum. Furthermore, we introduce the left and right Browder S -resolvent operators. Inspired by the S -resolvent equation, we give the Browder’s S -resolvent equation in quaternionic setting.