Norm closures of orbits of bounded operators

To every bounded linear operator $A$ between Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$ three cardinals $ι_r(A)$, $ι_i(A)$ and $ι_f(A)$ and a binary number $ι_b(A)$ are assigned in terms of which the descriptions of the norm closures of the orbits $\{G A L^{-1}:\ L \in \mathcal{G}_1,\ G \in \mathcal{G}_2\}$ are given for $\mathcal{G}_1$ 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.

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