We show that every Kubo-Ando operator mean of positive definite operators exists on the solvable Lie group of lower triangular matrices with positive diagonal entries. In particular, we show that the operator geometric mean of such lower triangular matrices appears as the common limit of the iteration process of the arithmetic and harmonic means. We further show that the iteration terminates in the finite number $\lceil\log_2 m \rceil$ of iterations for $m\times m$ lower unitriangular matrices and present its entrywise closed form for $m\leq 4.$
1
Dept. of Mathematics, Kyungpook National University, Daegu, South Korea
2
Dept. of Mathematics, Sungkyunkwan University, Suwon, South Korea
Hayoung Choi; Yongdo Lim. Operator Means of Lower Triangular Matrices. Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 175-190. http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a8/
@article{JOLT_2022_32_1_a8,
author = {Hayoung Choi and Yongdo Lim},
title = {Operator {Means} of {Lower} {Triangular} {Matrices}},
journal = {Journal of Lie Theory},
pages = {175--190},
year = {2022},
volume = {32},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a8/}
}
TY - JOUR
AU - Hayoung Choi
AU - Yongdo Lim
TI - Operator Means of Lower Triangular Matrices
JO - Journal of Lie Theory
PY - 2022
SP - 175
EP - 190
VL - 32
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a8/
ID - JOLT_2022_32_1_a8
ER -
%0 Journal Article
%A Hayoung Choi
%A Yongdo Lim
%T Operator Means of Lower Triangular Matrices
%J Journal of Lie Theory
%D 2022
%P 175-190
%V 32
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a8/
%F JOLT_2022_32_1_a8
