Measure, Integration & Real Analysis · Problem 10B.19

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · unitary-operators

Problem

Suppose TT is an invertible operator on a Hilbert space. Prove that TT is unitary if and only if ∥T∥=∥T−1∥=1\|T\| = \|T^{-1}\| = 1.

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