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Injective And Closed Range Iff Bounded Below

 
  • functional-analysis
  • Jan 16, 2024
a bounded linear map T between Banach spaces is injective with closed range if and only if it is bounded below show that T is injective and has closed range ⟺∃c>0,∀x∈E,∥T(x)∥≥c∥x∥
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