论文标题
希尔伯特太空运营商的球形aluthge变换的联合数值半径
Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators
论文作者
论文摘要
令$ \ mathbf {t} =（t_1，\ ldots，t_d）$为复杂的Hilbert Space $ \ Mathcal {H} $上的运算符的$ D $ -TUPLE。 $ \ mathbf {t} $的球形aluthge变换是$ \ \ wideHat {\ MathBf {t}}}给出的$ d $ - tuple：=（\ sqrt {p} v_1 v_1 v_1 \ \ sqrt {p} {p} $ p：= \ sqrt {t_1^*t_1+\ \ ldots+t_d^*t_d} $和$（v_1，\ ldots，v_d）$是一个联合部分等级，因此$ t_k = v_k p $ for $ 1 \ le K \ le K \ le d $。在本文中，我们证明了涉及$ \ wideHat {\ mathbf {t}} $的联合运算符规范的几种不等式。 Moreover, a characterization of the joint spectral radius of an operator tuple $\mathbf{T}$ via $n$-th iterated of spherical Aluthge transform is established.
Let $\mathbf{T}=(T_1,\ldots,T_d)$ be a $d$-tuple of operators on a complex Hilbert space $\mathcal{H}$. The spherical Aluthge transform of $\mathbf{T}$ is the $d$-tuple given by $\widehat{\mathbf{T}}:=(\sqrt{P}V_1\sqrt{P},\ldots,\sqrt{P}V_d\sqrt{P})$ where $P:=\sqrt{T_1^*T_1+\ldots+T_d^*T_d}$ and $(V_1,\ldots,V_d)$ is a joint partial isometry such that $T_k=V_k P$ for all $1 \le k \le d$. In this paper, we prove several inequalities involving the joint numerical radius and the joint operator norm of $\widehat{\mathbf{T}}$. Moreover, a characterization of the joint spectral radius of an operator tuple $\mathbf{T}$ via $n$-th iterated of spherical Aluthge transform is established.
