Uniqueness of Hahn–Banach extensions and some of its variants

In this paper, we analyze the various strengthening and weakening of uniqueness Hahn–Banach extension. addition, consider case in which Y is an ideal X. context, study property (U)/(SU)/(HB) (wU)/(k-U) for a subspace Banach space We obtain new characterizations these properties. different kinds stabilities resulting from properties tensor product spaces, spaces Bochner integrable functions, higher duals spaces. discuss examples classical where aforementioned are satisfied they fail. It established that hyperplane $$c_0$$ has (HB) if only it M-summand. observed finite-dimensional (k-U) , addition to ideal, then $$Y^*$$ k-strictly convex $$\ell _1$$ some natural k.