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Let $F$ be a complex Hilbert space and $\mathcal{B}(F)$ be the algebra of all bounded linear operators on $F$.
For ${\bf A} = (A_1,...,A_d) \in \mathcal{B}(F)^d$, the norm of ${\bf A}$ is given by
$$\|{\bf A}\|^2=\sum_{k=1}^d\|A_k\|^2.$$
For ${\bf T}=(T_1,...,T_d) \in \mathcal{B}(F)^d$ and ${...