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

✍ Scribed by Jiyuan Tao

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
200 KB
Volume
434
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 In(a) = In(x) whenever a • x > 0 by the min-max theorem of Hirzebruch, where the inertia of an element x in a Euclidean Jordan algebra is defined by In(x) := (π(x), ν(x), δ(x)), with π(x), ν(x), and δ(x) 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.

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