Smooth approximations of norms in separable Banach spaces

Abstract

Let X be a separable real Banach space having a k-times continuously Fr\'echet differentiable (i.e. Ck-smooth) norm where k=1,...,∞. We show that any equivalent norm on X can be approximated uniformly on bounded sets by Ck-smooth norms.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…