The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results
Takeaki Yamazaki
TL;DR
This paper explores the connection between the generalized Karcher equation and operator means, establishing Ando-Hiai inequalities for its solutions and examining properties of relative operator entropy.
Contribution
It introduces new inequalities related to the generalized Karcher equation and clarifies their relation to operator means and relative operator entropy.
Findings
Established two types of Ando-Hiai inequalities for solutions
Linked the generalized Karcher equation with operator means
Analyzed properties of relative operator entropy
Abstract
In this paper, we shall give a concrete relation between the generalized Karcher equation and operator means as its solution. Next, we shall show two types of the Ando-Hiai inequalities for the solution of the generalized Karcher equation. In this discussion, we also give a property of relative operator entropy.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Nonlinear Differential Equations Analysis