Method of continuity

In the mathematics of Banach spaces, the method of continuity provides sufficient conditions for deducing the invertibility of one bounded linear operator from that of another, related operator.

Let B be a Banach space, V a normed vector space, and ${\displaystyle (L_{t})_{t\in [0,1]}}$ a norm continuous family of bounded linear operators from B into V. Assume that there exists a constant C such that for every ${\displaystyle t\in [0,1]}$ and every ${\displaystyle x\in B}$

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