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Jul 24, 2019 at 23:59 comment added Fabian Wirth I do. This follows from your arguments if you note that from the definition already $\liminf$ and $\limsup$ are closed.
Jul 24, 2019 at 23:32 comment added Mike Van Thank you so much. I had been coffused about that proof for weeks. I think that the claim is true if we change $\sigma_1(T)$ by $\overline{ \sigma_1(T)}$. You agree with me?
Jul 24, 2019 at 23:17 vote accept Mike Van
Jul 24, 2019 at 23:04 history answered Fabian Wirth CC BY-SA 4.0