Measure, Integration & Real Analysis · Problem 6D.15

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · open-ball-not-containing-origin

Problem

Suppose

B

is an open ball in a normed vector space

V

such that

0 \notin B

. Prove that there exists

\varphi \in V'

such that

\operatorname{Re} \varphi(f) > 0

for all

f \in B