Theorems · Theorem · functional analysis
IsBoundedLinearMap.bound
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : Module 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : Module 𝕜 F] {f : E → F},
IsBoundedLinearMap 𝕜 f → ∃ M, 0 < M ∧ ∀ (x : E), ‖f x‖ ≤ M * ‖x‖- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- IsBoundedLinearMapstatement and proof · cited by 39
Cited by4
Results whose statement or proof uses this declaration.
- spectralNorm_uniqueproof · cited by 3
- IsBoundedLinearMap.negproof · cited by 2
- IsBoundedLinearMap.isBigO_idproof · cited by 1
- isBoundedLinearMap_iffproof · cited by 0