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The Modified Heinz’s Inequality

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DOI: 10.4236/jamp.2013.15010    3,050 Downloads   4,909 Views  
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ABSTRACT


In my paper [1], we aimed to determine the best possible range of r such that the modified Heinzs 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.


Conflicts of Interest

The authors declare no conflicts of interest.

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.

  
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