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Keywords

Positive definite matrix, Positive linear map, Operator monotone function, Connection, α-Arithmetic (α-Geometric, α-Harmonic) operator mean, Generalized inverse of linear operator.

Abstract

In this note, generalized connections σ_{T ,f} are investigated, where Aσ_{T ,f} B = T_Af(T_A)^−(B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J → R on an interval J ⊂ R. Here the symbol (T_A)^− denotes a reflexive generalized inverse of a positive bounded linear operator T_A. The problem of estimating a given generalized connection by other ones is studied. The obtained results are specified for special cases of α-arithmetic, α-geometric and α-harmonic operator means.

abs_vol30_pp494-506.pdf (30 kB)
Abstract

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