Numerical radius inequalities for tensor product of operators
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929456330833920 |
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| author | Sen, Anirban Bhunia, Pintu Paul, Kallol |
| author_facet | Sen, Anirban Bhunia, Pintu Paul, Kallol |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2203_12162 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Numerical radius inequalities for tensor product of operators Sen, Anirban Bhunia, Pintu Paul, Kallol Functional Analysis Primary 47A12, Secondary 15A60, 47A30, 47A50 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. |
| title | Numerical radius inequalities for tensor product of operators |
| topic | Functional Analysis Primary 47A12, Secondary 15A60, 47A30, 47A50 |
| url | https://arxiv.org/abs/2203.12162 |