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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2009.1
- 수록면
- 167 - 181 (15page)
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초록· 키워드
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Based on Ricatti equation XA-1X = B for two (positive invertible) operators
A and B which has the geometric mean A#B as its solution, we consider a cubic equation
X(A#B)-1X(A#B)-1X = C
for A,B and C. The solution X = (A#B)# 1/3C is a candidate of the geometric mean of
the three operators. However, this solution is not invariant under permutation unlike the
geometric mean of two operators. To supply the lack of the property, we adopt a limiting
process due to Ando-Li-Mathias. We define reasonable geometric means of k operators for
all integers k ≥ 2 by induction. For three positive operators, in particular, we define the
weighted geometric mean as an extension of that of two operators
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참고문헌 (19)
참고문헌 신청
B. Q. Feng / 2005 / Geometric means and Hadamard products / Math. Inequalities Appl 8 : 559 ~ 564
E. Andruchow / 1999 / Geometrical signi cance of the Lowner- Heinz inequality / Proc. Amer. Math. Soc 128 : 1031 ~ 1037
F. Kubo / 1980 / Means of positive linear operators / Math. Ann 246 : 205 ~ 224
G. Corach / 1994 / Convexity of the geodestic distance on spaces of positive operators / Illinois J. Math 38 : 87 ~ 94
H. Kosaki / 1984 / Geometric mean of several positive operators
E. Andruchow / 1999 / Geometrical signi cance of the Lowner- Heinz inequality / Proc. Amer. Math. Soc 128 : 1031 ~ 1037
F. Kubo / 1980 / Means of positive linear operators / Math. Ann 246 : 205 ~ 224
G. Corach / 1994 / Convexity of the geodestic distance on spaces of positive operators / Illinois J. Math 38 : 87 ~ 94
H. Kosaki / 1984 / Geometric mean of several positive operators
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