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arXiv · 1702.08671

On The Absolute Value of The Product and the Sum of Linear Operators

Mohammed Hichem Mortad
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Abstract

Let $A,B\in B(H)$. In the present paper, we establish simple and interesting facts on when we have $|A||B|=|B||A|$, $|AB|=|A||B|$, $|A\pm B|\leq |A|+|B|$, $||A|-|B||\leq |A\pm B|$ and $\||A|-|B|\|\leq \|A\pm B\|$, where $|\cdot|$ denotes the absolute value (or modulus) of an operator. The results give some other interesting consequences.

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Mohammed Hichem Mortad. 2017-02-28. On The Absolute Value of The Product and the Sum of Linear Operators. https://arxiv.org/abs/1702.08671

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