Distortion problem
In functional analysis, a branch of mathematics, the distortion problem is to determine by how much one can distort the unit sphere in a given Banach space using an equivalent norm. Specifically, a Banach space X is called λ-distortable if there exists an equivalent norm |x| on X such that, for all infinite-dimensional subspaces Y in X, sup y 1 , y 2 ∈ Y , ‖ y i ‖ = 1 | y 1 | | y 2 | ≥ λ {\displaystyle \sup _{y_{1},y_{2}\in Y,\|y_{i}\|=1}{\frac {|y_{1}|}{|y_{2}|}}\geq \lambda } (see distortion (mathematics)).