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arXiv · 2203.12162

Numerical radius inequalities for tensor product of operators

Anirban Sen·Pintu Bhunia·Kallol Paul
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Abstract

The two well-known numerical radius inequalities for the tensor product $A \otimes B$ acting on $\mathbb{H} \otimes \mathbb{K}$, where $A$ and $B$ are bounded linear operators defined on complex Hilbert spaces $\mathbb{H} $ and $ \mathbb{K},$ respectively are, $ \frac{1}{2} \|A\|\|B\| \leq w(A \otimes B) \leq \|A\|\|B\| $ and $w(A)w(B) \leq w(A \otimes B) \leq \min \{ w(A) \|B\|, w(B) \|A\| \}. $ In this article we develop new lower and upper bounds for the numerical radius $w(A \otimes B)$ of the tensor product $A \otimes B $ and study the equality conditions for those bounds.

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Anirban Sen, Pintu Bhunia, Kallol Paul. 2022-03-23. Numerical radius inequalities for tensor product of operators. https://doi.org/10.1007/s12044-022-00722-2

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