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##### Trace inequalities for logarithms and powers of J-Hermitian matrices

**Authors**: Bebiano N, Lemos R, da Providencia J, , Soares G

**Ref.**: LINEAR ALGEBRA AND ITS APPLICATIONS **432**, 3172 (2010)

**Abstract**: Spectral inequalities are stated for the trace of the exponential or the logarithmic of certain J-Hermitian matrices, J = I-r circle plus -In-r, 0 < r < n. The obtained inequalities are established in the context of indefinite inner product spaces, and they are known to be valid for Hilbert space operators or operator algebras.