The Modified Heinz’s Inequality
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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.
Keywords:
Heinz’s Inequality
Cite this paper:
Yoshino, T. (2013) The Modified Heinz’s Inequality. Journal of Applied Mathematics and Physics, 1, 65-70. doi: 10.4236/jamp.2013.15010.
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.