3 problems

Let $X$ be a Banach space. It is said to fail the Radon–Nikodým property (RNP) if $X$ does not have the RNP, and an equivalent renorming is a norm on $X$ equivalent to its original…

Let $G$ be a group and let $X$ be a real Banach space with $\dim X \geqslant |G|$. An equivalent renorming of $X$ is a norm equivalent to its original norm, and…

Let $X$ be a Banach space and let $G$ be a group. A group is represented on $X$ if it is isomorphic to a group of linear isometries of some equivalent norm on $X$. Jarosz's represe…