Theorems · Theorem · functional analysis

ContinuousLinearMap.toSesqForm_apply_norm_le

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {E' : Type u_4} [inst_3 : SeminormedAddCommGroup E'] [inst_4 : InnerProductSpace 𝕜 E'] {f : E →L[𝕜] E'} {v : E'},
  ‖(ContinuousLinearMap.toSesqForm f) v‖ ≤ ‖f‖ * ‖v‖

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

0 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace