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Quotient Map is a Contraction Operator

Last updated Nov 1, 2022

# Statement

Let (X,)(X, ||\cdot||) be a Banach Space

Banach Space

Definition A is a that is a ....

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and let YXY \subset X be a Closed

Closed

Definition Suppose (X,τ)(X, \tau) is a . Then KXK \subset X is if KCK^{C} is ....

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Vector Subspace

Vector Subspace

Definition Suppose VV is a over FF. Supppose WVW \subset V and WW is a over FF when...

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. Then the Quotient Map J:XX/YJ : X \to X / Y defined as J(x):=[x]J(x) := [x] is a Bounded Linear Operator and J1||J|| \leq 1.

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