Let $A$ and $B$ be unital Banach algebras and $\theta : A\to B$ a surjective homomorphism between these two spaces. What is a sufficient requirement for $\theta$ being bounded, and how would a proof (sketch) look like?
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Markus Klyver
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I just wanted to point out that you can avoid the discussion of surjectivity by replacing B with the image of A. So you can look for conditions on $\theta$ and its image that guarantee continuity. There’s some discussion of the existence of discontinuous homomorphisms here: https://math.stackexchange.com/questions/11537/is-there-an-algebraic-homomorphism-between-two-banach-algebras-which-is-not-cont – Josh Keneda Apr 05 '19 at 20:42