Document Zbl 1297.15023

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On \(f\)-connections of positive definite matrices. (English) Zbl 1297.15023

Ann. Funct. Anal. 5, No. 2, 147-157 (2014).

Summary: By using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use \(\alpha \)-arithmetic, \(\alpha \)-geometric and \(\alpha \)-harmonic operator means.

MSC:

15A45	Miscellaneous inequalities involving matrices
15B48	Positive matrices and their generalizations; cones of matrices
47A64	Operator means involving linear operators, shorted linear operators, etc.

Keywords:

positive definite matrix; \(\alpha \)-arithmetic operator mean; \(\alpha \)-geometric operator mean; \(\alpha \)-harmonic operator mean; positive linear map; operator monotone function; \(f\)-connection

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