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Theorems · Theorem · operator theory

LinearPMap.adjoint.congr_simp

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F]
  (T T_1 : E →ₗ.[𝕜] F), T = T_1 → ∀ [inst_5 : CompleteSpace E], T.adjoint = T_1.adjoint
Defined in
Mathlib.Analysis.InnerProductSpace.LinearPMap
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Foundations
Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceCompleteSpace
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RingHom.id · cited by 18349RingHom.idNormedAddCommGroup · cited by 15752NormedAddCommGroupInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeCompleteSpace · cited by 2532CompleteSpaceLinearPMap · cited by 179LinearPMapLinearPMap.adjoint · cited by 13LinearPMap.adjointadjoint.congr_simpCITED BYCITES

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