Linear Algebra Done Right · Problem 6A.4

Inner Product Spaces — Sheldon Axler

Mathematics — Linear Algebra · inner-products-and-norms

Problem

Suppose

T \in \mathcal{L}(V)

is such that

\|Tv\| \leq \|v\|

for every

v \in V

. Prove that

T - \sqrt{2}\, I

is injective.