Norm closures of orbits of bounded operators

Abstract

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 $\{GA{L}^{-1}:L\in {\mathcal{G}}_1,G\in {\mathcal{G}}_2\}$ 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.

19 pages

References in corpus (1)

• Metric and homogeneous structure of closed range operators

Cited by in corpus (1)

• Borel structure of the spectrum of a closed operator