Some exponential inequalities for Semisimple Lie group
نویسنده
چکیده
Let ‖| · ‖| be any give unitarily invariant norm. We obtain some exponential relations in the context of semisimple Lie group. On one hand they extend the inequalities (1) ‖|e‖| ≤ ‖|eReA‖| for all A ∈ Cn×n, where ReA denotes the Hermitian part of A, and (2) ‖|e‖| ≤ ‖|ee‖|, where A and B are n×n Hermitian matrices. On the other hand, the inequalities of Weyl, Ky Fan, Golden-Thompson, Lenard-Thompson, Cohen, and So-Thompson are recovered. Araki’s relation on (eee) and eee, where A, B are Hermitian and r ∈ R, is extended.
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