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 $\{ G A L^{ -1}:\ L \in \mathcal{ G}_1,\ G \in \mathcal{ G}_2\}$ 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.
Categories: math.FA