Weighted geometric mean of n-operators with n-parameters

Changdo Jung; Hosoo Lee; Yongdo Lim; Takeaki Yamazaki

doi:10.1016/j.laa.2009.11.013

Weighted geometric mean of n-operators with n-parameters

Changdo Jung
, Hosoo Lee
, Yongdo Lim
, Takeaki Yamazaki

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We shall consider a weighted geometric mean of n-operators with n-parameters. It is based on the geometric mean defined in our previous paper [C. Jung, H. Lee, T. Yamazaki, On a new construction of geometric mean of n-operators, Linear Algebra Appl. 431 (2009) 1477-1488]. Then we shall show that its weights can be obtained by simple forms in the commutative operators case. Some properties of the weighted geometric mean are obtained.

Original language	English
Pages (from-to)	1515-1530
Number of pages	16
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	6
DOIs	https://doi.org/10.1016/j.laa.2009.11.013
State	Published - 1 Mar 2010
Externally published	Yes

Keywords

Geometric mean of n-operators
Positive operators
Thompson metric
Weighted geometric mean of n-operators

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10.1016/j.laa.2009.11.013

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AU - Jung, Changdo

AU - Lee, Hosoo

AU - Lim, Yongdo

AU - Yamazaki, Takeaki

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Y1 - 2010/3/1

N2 - We shall consider a weighted geometric mean of n-operators with n-parameters. It is based on the geometric mean defined in our previous paper [C. Jung, H. Lee, T. Yamazaki, On a new construction of geometric mean of n-operators, Linear Algebra Appl. 431 (2009) 1477-1488]. Then we shall show that its weights can be obtained by simple forms in the commutative operators case. Some properties of the weighted geometric mean are obtained.

AB - We shall consider a weighted geometric mean of n-operators with n-parameters. It is based on the geometric mean defined in our previous paper [C. Jung, H. Lee, T. Yamazaki, On a new construction of geometric mean of n-operators, Linear Algebra Appl. 431 (2009) 1477-1488]. Then we shall show that its weights can be obtained by simple forms in the commutative operators case. Some properties of the weighted geometric mean are obtained.

KW - Geometric mean of n-operators

KW - Positive operators

KW - Thompson metric

KW - Weighted geometric mean of n-operators

UR - https://www.scopus.com/pages/publications/72949102628

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JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 6

ER -

Weighted geometric mean of n-operators with n-parameters

Abstract

Keywords

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