Theorems · Theorem · functional analysis
SeparationQuotient.norm_normedMk_le
∀ {M : Type u_1} [inst : SeminormedAddCommGroup M], ‖SeparationQuotient.normedMk‖ ≤ 1The operator norm of the projection is at most 1.
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- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- zero_le_oneproof · cited by 316
- NormedAddGroupHomstatement · cited by 216
- SeparationQuotientstatement · cited by 128
- NormedAddGroupHom.opNorm_le_boundproof · cited by 12
- SeparationQuotient.normedMkstatement and proof · cited by 5
- SeparationQuotient.normedMk_applyproof · cited by 3
- SeparationQuotient.mkAddMonoidHom_applyproof · cited by 2
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