Linear Algebra Done Right · Problem 7F.23

Operators on Complex Vector Spaces — Sheldon Axler

Mathematics — Linear Algebra · operator-norms-continuity

Problem

Suppose

T \in \mathcal{L}(V, W)

. Show that

T

is uniformly continuous with respect to the metrics on

V

and

W

that arise from the norms on those spaces (see Exercise 23 in Section 6B).