A note on the Ostrowski–Schneider type inertia theorem in Euclidean Jordan algebras

Abstract: In a recent paper [7], Gowda et al. extended Ostrowski–Schneider type inertia results to certain linear transformations on Euclidean Jordan algebras. In particular, they showed that whenever by the min–max theorem of Hirzebruch, where the inertia of an element x in a Euclidean Jordan algebra is defined bywith , , and denoting, respectively, the number of positive, negative, and zero eigenvalues, counting multiplicities. In this paper, we present a Peirce decomposition version of Wimmer’s result [13] and show that it is equivalent to the above result. In addition, we extend Higham and Cheng’s result ([8], Lemma 4.2) to the setting of Euclidean Jordan algebras. [Copyright &y& Elsevier]