arXiv 0812.08862008-12-04math.OAmath.FA

An operator extension of Bohr's inequality

M. S. Moslehian, J. Pecaric, I. Peric

备注：: 7 Pages, to appear in Bull. Iranian Math. Soc
发表信息：: Bull. Iranian Math. Soc. 35 (2009), no. 2, 67-74

英文摘要：

We establish an operator extension of the following generalization of Bohr's inequality, due to M.P. Vasić and D.J. Kečkić: $$|\sum_{i=1}^n z_i|^r \leq (\sum_{i=1}^n α_i^{1/(1-r)})^{r-1}\sum_{i=1}^n α_i|z_i|^r \quad (r>1, z_i \in{\mathbb C}, α_i>0, 1 \leq i \leq n) .$$ We also present some norm inequalities related to our noncommutative generalization of Bohr's inequality.

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