Timeline for What is known about $\operatorname{gap}(A) = \|A\| - r(A)$ for bounded operators on Hilbert spaces?
Current License: CC BY-SA 4.0
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| Apr 5 at 9:18 | comment | added | Geoff Robinson | Notice that a nilpotent operator $A$ has $r(A) = 0,$ whereas $\|A\|$ can be arbitrarily large, so I wonder what sort of answer you would regard as useful in your context? | |
| Apr 4 at 14:48 | comment | added | Gerald Edgar | I think you need to consider related operators $B = S^{-1}AS$, where $S$ is invertible. The spectral radius for $B$ is the same as for $A$, but the norm may be different. I believe (I read somewhere long ago?) the infimum of all these norms is the spectral radius. | |
| Apr 4 at 14:10 | history | asked | stoic-santiago | CC BY-SA 4.0 |