论文标题
用于操作员张量产品的数值半径不平等
Numerical radius inequalities for tensor product of operators
论文作者
论文摘要
张量产品$ a \ otimes b $作用于$ \ mathbb {h} \ otimes \ mathbb {k} $的两个众所周知的数值半径不平等，其中$ \ a $ a $ a $ a和$ b $是在复杂的hilbert space $ \ mathbb $ \ mathbb和$ math $ { \ frac {1} {2} \ | a \ | \ | b \ | \ leq w（a \ otimes b）\ leq \ | a \ | \ | b \ | $和$ w（a）w（b）\ leq w（a \ otimes b）\ leq \ min \ {w（a）\ | b \ |，w（b）\ | a \ | \}。 $在本文中，我们为张量产品$ a \ otimes b $的数值半径$ w（a \ otimes b）$开发了新的下层和上限，并研究了这些界限的平等条件。
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.
