The Modified Heinz’s Inequality ()
Abstract
In my paper [1], we aimed to
determine the best possible range of r such that the modified Heinz’s inequality holds for any bounded linear operators A and B on a Hilbert space H such as and for any given a and b such as a>0 and b>0. But the counter-examples prepared in [1] and also in [2]
were not sufficient and, in this paper, we shall constitute the sufficient
counter-examples which will satisfy all the lacking parts.
Share and Cite:
Yoshino, T. (2013) The Modified Heinz’s Inequality.
Journal of Applied Mathematics and Physics,
1, 65-70. doi:
10.4236/jamp.2013.15010.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
T. Yoshino, “A Modified Heinz’s Inequality,” Linear Algebra and its Applications, Vol. 420, No. 2-3, 2007, pp. 686-699. http://dx.doi.org/10.1016/j.laa.2006.08.031
|
[2]
|
T. Yoshino, “The Best Possible Range of a Modified Heinz’s Inequality,” International Journal of Funct. Anal. Oper. Theory Appl., Vol. 3, No. 1, 2011, pp. 1-7.
|