Measure, Integration & Real Analysis · Problem 10A.8

Linear Maps on Hilbert Spaces — Sheldon Axler

Mathematics — Measure Theory · left-right-invertibility-adjoint

Problem

Suppose

T

is a bounded operator on a Hilbert space. (a) Prove that

T

is left invertible if and only if

T^*

is right invertible. (b) Prove that

T

is invertible if and only if

T

is both left and right invertible.