Characterization of subspace

Functional Analysis
Post Reply
Papapetros Vaggelis
Community Team
Posts: 426
Joined: Mon Nov 09, 2015 1:52 pm

Characterization of subspace

#1

Post by Papapetros Vaggelis »

Let \(\displaystyle{\left(X,||\cdot||\right)}\) be an \(\displaystyle{\mathbb{R}}\) - normed space and \(\displaystyle{Y}\)

be \(\displaystyle{\mathbb{R}}\) - linear subspace of \(\displaystyle{X}\) . Show that

$$\overline{Y}=\cap\,\left\{\rm{Ker}(f): f\in X^{\star}\,,Y\subseteq \rm{Ker}(f)\right\}$$
Post Reply

Create an account or sign in to join the discussion

You need to be a member in order to post a reply

Create an account

Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute

Register

Sign in

Who is online

Users browsing this forum: No registered users and 8 guests