Abstract
The main goal of this article is to present new inequalities for the spectral geometric mean A ♮ t B of two positive definite operators A, B on a Hilbert space. The obtained results complement many known inequalities for the geometric mean A ♯ t B . In particular, explicit comparisons between A ♮ t B and A ♯ t B are given, with applications towards Ando-type inequalities and Ando-Hiai inequalities for A ♮ t B and some other consequences.
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