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How do you compute the dual norm of an induced norm on a subspace of a finite-dimensional $\ell^p$-normed vector space?

Say you have a finite-dimensional vector space $V$ with an $\ell^p$ norm on it. In general, the norm induced on a subspace $V_s$ of doesn't have to be another $\ell^p$ norm, so the unit sphere in $V_s$...
Mike Battaglia's user avatar