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

Invariance of the essential spectra of operator pencils

The essential spectrum of operator pencils with bounded coefficients in a Hilbert space is studied. Sufficient conditions in terms of the operator coefficients of two pencils are derived which guarantee the same essential spectrum. This is done by exploiting a strong relation between an operator pencil and a specific linear subspace (linear relation)

Erratum to: 36th International Symposium on Intensive Care and Emergency Medicine

[This corrects the article DOI: 10.1186/s13054-016-1208-6.]