  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.
