graphon shift operators are self-adjoint

[[concept]]

Theorem

Let $W$ be a graphon and $T_{W}$ its graphon shift operator. Then $T_{W}$ is self-adjoint.

Proof

graphons are symmetric. So

⟨ T_{W} x, y ⟩ = ⟨ x, T_{W} y ⟩

Review

graphon shift operators are {self-adjoint} because graphons are {symmetric functions}

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2025-03-31 lecture 16

Created 2025-03-31 Last Modified 2025-05-30