Let $K$ be $\mathbb{R}$ or $\mathbb{C}$. A Banach space $X$ over $K$ is stable if $X\cong X\times K$. I encountered the following question in some papers in the sixties:



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> Is every infinite dimensional Banach space stable?
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> 
> 


Is this question still open?



Do non-stable Banach spaces exist?
No, see the following paper of Gowers


<https://blms.oxfordjournals.org/content/26/6/523.full.pdf>


