Adjoint operator

Let $𝑇 : 𝑋 \to 𝑋$ be an unbounded operator on a Hilbert space. An unbounded operator $𝐴 †$ is its adjoint iff #m/def/anal/fun

⟨ 𝑥 | 𝐴 𝑦 ⟩ = ⟨ 𝐴 † 𝑥 | 𝑦 ⟩

for all $𝑥 \in d o m 𝐴 †$ and $𝑦 \in d o m 𝐴$ , and any $(𝐵 †) †$ is a restriction of $𝐴$ .

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