Theorems · Theorem · functional analysis

ContinuousLinearMap.adjoint_comp_self_eq_zero_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
  [inst_5 : CompleteSpace E] [inst_6 : CompleteSpace F] {A : E →L[𝕜] F}, ContinuousLinearMap.adjoint A ∘SL A = 0 ↔ A = 0

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

0 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceInnerProductSpaceCompleteSpaceCompleteSpace