- #1

joshmccraney

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## Homework Statement

Given two linear self-adjoint operators ##A,B##, is it true ##AB## is also self-adjoint.

## Homework Equations

Self adjoint implies ##(A[f],g) = (f,A[g])##

## The Attempt at a Solution

I'm not really sure. I'm stuck almost right away: ##(AB[f],g) = (A[B[f]],g) = (B[f],Ag) = (f,BAg) = (f,ABg)##. Last equality is from linearity of ##B,A##. The first few steps I think follow from self-adjoint of ##A,B##.

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