Norm closures of orbits of bounded operators

To every bounded linear operator $A$ between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$ three cardinals ${\iota }_r(A)$, ${\iota }_i(A)$ and ${\iota }_f(A)$ and a binary number ${\iota }_b(A)$ are assigned in terms of which the descriptions of the norm closures of the orbits ${G A L^{-1}:\ L \in $\mathcal{G}$_1,\ G \in $\mathcal{G}$_2}$aregivenfor$$\mathcal{G}$_1$and$$\mathcal{G}$_2$ (chosen independently) being the trivial group, the unitary group or the group of all invertible operators on $\mathcal{H}$ and $\mathcal{K}$, respectively.