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Weighted Lim's Geometric Mean of Positive Invertible Operators on a Hilbert Space.
- Source :
-
Journal of Computational Analysis & Applications . Mar2021, Vol. 29 Issue 2, p390-400. 11p. - Publication Year :
- 2021
-
Abstract
- We generalize the weighted Lim's geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim's ge- ometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-Pálfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HILBERT space
*HERMITIAN operators
*UNITARY operators
*BIJECTIONS
*ARITHMETIC mean
Subjects
Details
- Language :
- English
- ISSN :
- 15211398
- Volume :
- 29
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Computational Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 141659016