Index of Notation

$\mathcal{B}\left(\mathcal{H}\right)$

Hilbert space

$M_{m\mathrm{,}n}\left(V\right)$

m by n matrix space over V

$C_0\left(\Omega \right)$

Space of continuous complex functions vanishing at $\infty$ on $\Omega$

$\Vert \alpha \Vert$

Matrix norm of $\alpha$

$\langle v\mathrm{,}w\rangle$

Scalar pairing of matrices

$\langle \langle v\mathrm{,}w\rangle \rangle$

Matrix pairing of matrices

$\left(V\mathrm{,}{\mathcal{O}}_n\right)$

Operator space

$\left(V\mathrm{,}{\mathcal{W}}_n\right)$

Numerical radius operator space

$\omega (\cdot )$

Numerical radius norm on $\mathcal{B}\left(\mathcal{H}\right)$

$B\left(V\mathrm{,}W\right)$

Space of bounded mappings

$B^{\sigma }\left(V\mathrm{,}W\right)$

Space of w*-bounded mappings

$CB\left(V\mathrm{,}W\right)$

Space of completely bounded mappings

$\mathcal{W}CB\left(V\mathrm{,}W\right)$

Space of $\mathcal{W}$ -completely bounded mappings