Normed

Results named in Tau Ceti's TauCeti.Analysis.Normed modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

Banach's lemma to Neumann series criterion…

• Banach's lemma
• Banach–Steinhaus theorem (Uniform Boundedness Principle) over a Tate ring
• Bounded Inverse Theorem
• Closed Graph Theorem for normed modules over a Tate ring
• The continuous first isomorphism theorem for Banach algebras
• Cramer's rule bound
• The Duhamel identity for the exponential of a bounded operator
• Ehrling's inequality
• Gantmacher's criterion
• Gantmacher's theorem
• Gelfand's formula in a nonunital complex Banach algebra
• Grothendieck's lemma
• Hölder's inequality for weak norms
• Johnson's theorem
• Johnson's uniqueness-of-norm theorem
• Johnson–Sinclair theorem, nonunital form
• Local Neumann formula for the resolvent
• Mazur's lemma, in sequential form
• The method of continuity (Gilbarg–Trudinger, Theorem 5.2)
• Neumann series criterion (TauCeti.IsNormMulUnit.of_norm_sub_lt)

Norm double-annihilator theorem to Šmulian's theorem

• Norm double-annihilator theorem
• Open Mapping Theorem for normed modules over a Tate ring
• The quadratic Taylor estimate for the exponential
• Quantitative Open Mapping Theorem
• Rickart's scalar-commutant theorem
• Riesz's lemma, translated form
• Schauder's theorem
• Schur's theorem (lp.tendsto_of_tendsto_toWeakSpace_one)
• Sequential Closed Graph Theorem for normed modules over a Tate ring
• Serre's potential orthonormalisation theorem
• The Singer–Wermer theorem
• Ultrametric Neumann estimate
• Young's inequality
• Šilov's theorem
• Šmulian's theorem

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