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Sagae-Tanabe Weighted Means and Reverse Inequalities

김세정|이호수|임영도|안은경
경북대학교 자연과학대학 수학과|2007.12|Kyungpook Mathematical Journal|제47권 제4호|pp. 595-600

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참고문헌

키워드

Sagae-Tanabe geometric meanThompson metricSpecht ratiooperator inequality.
주제분류수학

초록

In this paper we consider weighted arithmetic and geometric means of several positive definite operators proposed by Sagae and Tanabe and we establish a reverse inequality of the arithmetic and geometric means via Specht ratio and the Thompson metric on the convex cone of positive definite operators.

Abstract

In this paper we consider weighted arithmetic and geometric means of several positive definite operators proposed by Sagae and Tanabe and we establish a reverse inequality of the arithmetic and geometric means via Specht ratio and the Thompson metric on the convex cone of positive definite operators.

참고문헌 (11)

  1. "An extended Lie-Trotter formula and its applications", 427, pp.190~196 (2007)
  2. "On the geometric-arithmetic meaninequality for matrices", 2, pp.125~128 (1997)
  3. "Geometic means", 385, pp.305~334 (2004)
  4. "Convexity of the geodesic distance on spaces ofpositive operators", illi(is j), pp.87~94 (1994)
  5. "A reverse inequality for theweighted geometric mean due to Lawson-Lim", 427, pp.272~284 (2007)
  6. "Kantorovich type operator inequalities via theSpecht ratio", 377, pp.69~81 (2004)
  7. "A sharp converse inequality of thre weighted arith-metic and geometric means of positive denite operators to appear in MathematicalInequalities and Applications"
  8. "A converse inequality of higher-order weighted arithmetic andgeometric means of positive denite operators", 426, pp.490~496 (2007)
  9. "Symmetric spaces with convex metrics", 19, pp.571~602 (2007)
  10. "Metric onvexity of symmetric cones", 44, pp.1~22 (2007)
  11. "D.Lawson and Y", a general framework for extending means to higher orders

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