/sci/ - Science & Math

Hey lads. I've recently been studying eigentheory and fixed points, and I've noticed some very interesting patterns, so I'd like to make a conjecture: Every linear endomorphism of a Banach space has at least one fixed point.
The best I've been able to do is show that, for isometries on finite-dimensional spaces, Brouwer's fixed point theorem gives us the result immediately, since the linear isometry fixes the unit ball.
I think that the essence of the problem is framing it in its proper categorical context. Any suggestions?

>>11421257
L'Hospital is one of, if not the single most convenient theorem in calculus, it's extremely intuitive, and I don't care if autists in France don't learn about it and proceed to do disgusting algebraic arguments.

>>11380785
Correct and Microfoundations-pilled.