# Commit 2021-12-24 16:32 3377bccd

View on Github →feat(analysis/inner_product_space/adjoint): define the adjoint of a continuous linear map between Hilbert spaces (#10825)
This PR defines the adjoint of an operator `A : E →L[𝕜] F`

as the unique operator `adjoint A : F →L[𝕜] E`

such that `⟪x, A y⟫ = ⟪adjoint A x, y⟫`

for all `x`

and `y`

. We then use this to put a star algebra structure on `E →L[𝕜] E`

with the adjoint as the star operation (while leaving the C* property for a subsequent PR).