Functional analysis MOC

Adjoint operator

Let 𝑇 :𝑋 →𝑋 be an unbounded operator on a Hilbert space. An unbounded operator 𝐴† is its adjoint iff fun

⟨𝑥|𝐴𝑦⟩=⟨𝐴†𝑥|𝑦⟩

for all 𝑥 ∈dom⁡𝐴† and 𝑦 ∈dom⁡𝐴, and any (𝐵†)† is a restriction of 𝐴.

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