Theorems in functional analysis | Operator theory

Bounded inverse theorem

In mathematics, the bounded inverse theorem (or inverse mapping theorem) is a result in the theory of bounded linear operators on Banach spaces. It states that a bijective bounded linear operator T from one Banach space to another has bounded inverse Tโˆ’1. It is equivalent to both the open mapping theorem and the closed graph theorem. (Wikipedia).

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Related pages

Bijection | Inverse function | Banach space | Mathematics | Lp space | Homeomorphism | Open mapping theorem (functional analysis) | Logical equivalence | Baire space | Closed graph theorem | Sequence | Topological vector space