| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
We found a multivariate extension of Golden-Thompson’s trace inequality, which may be considered as an interpolation inequality between Golden-Thompson’s inequality and Jensen’s inequality, and we extended the two variable Golden-Thompson inequality to deformed exponentials. We proposed a general procedure to construct multivariate geometric means based on the theory of perspectives of regular operator maps. The method is general enough to encompass all known examples of multivariate geometric means, and it also provides new interesting examples. A novel feature is that we may impose an updating procedure adapted to data acquisition. We characterised the von Neumann entropy as the only possible entropic measure satisfying two fundamental properties coming from thermodynamics. We obtained an inequality for expectations of means of positive random variables.
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