Operator space approach to steering inequality

An Operator Inequality Related to Jensen’s Inequality

For bounded non-negative operators A and B, Furuta showed 0 ≤ A ≤ B implies A r 2BA r 2 ≤ (A r 2BA r 2 ) s+r t+r (0 ≤ r, 0 ≤ s ≤ t). We will extend this as follows: 0 ≤ A ≤ B ! λ C (0 < λ < 1) implies A r 2 (λB + (1− λ)C)A r 2 ≤ {A r 2 (λB + (1 − λ)C)A r 2 } s+r t+r , where B ! λ C is a harmonic mean of B and C. The idea of the proof comes from Jensen’s inequality for an operator convex functio...

Temporal steering inequality

Yueh-Nan Chen,1,2,* Che-Ming Li,3,† Neill Lambert,2,‡ Shin-Liang Chen,1 Yukihiro Ota,2 Guang-Yin Chen,4 and Franco Nori2,5 1Department of Physics and National Center for Theoretical Sciences, National Cheng-Kung University, Tainan 701, Taiwan 2CEMS, RIKEN, Wako-shi, Saitama 351-0198, Japan 3Department of Engineering Science, National Cheng-Kung University, Tainan City 701, Taiwan 4Department of...

An Operator Extension of Bohr's inequality

Some complementary inequalities to Jensen’s operator inequality

In this paper, we study some complementary inequalities to Jensen's inequality for self-adjoint operators, unital positive linear mappings, and real valued twice differentiable functions. New improved complementary inequalities are presented by using an improvement of the Mond-Pečarić method. These results are applied to obtain some inequalities with quasi-arithmetic means.

non-corrective approach to pronunciation

the aim of this study has been to find answers for the following questions: 1. what is the effect of immediate correction on students pronunciation errors? 2. what would be the effect of teaching the more rgular patterns of english pronunciation? 3. is there any significant difference between the two methods of dealing with pronuciation errore, i. e., correction and the teaching of the regular ...