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Quotient Normed Vector Space

Last updated Nov 1, 2022

# Definition

Let $(X, ||\cdot||)$ be a Normed Vector Space

and let

Y \subset X

be a Closed Vector Subspace. Then we call the Quotient Vector Space

X / Y

endowed with the Quotient Norm

||[\cdot]||

Quotient Normed Vector Space.

# Remarks

The requirement that $Y$ is Closed

Closed

Definition Suppose $(X, \tau)$ is a . Then $K \subset X$ is if $K^{C}$ is ....

11/7/2022

is very important. See Quotient Norm

Quotient Norm

Statement Let $(X, ||\cdot||)$ be a and let $Y \subset X$ be a . Then $||[\cdot]|| : X /...

11/7/2022

Backlinks

Quotient Normed Space of a Banach Space is Banach

Quotient Normed Space of a Banach Space is Banach

...||\cdot||)$ be a and let $Y \subset X$ be a . Then the $(X / Y, ||[\cdot]||)$ is a . Proof use [ ] [ ] Use definition to get close and then use......

11/7/2022
Quotient Normed Vector Space

Quotient Normed Vector Space

...Let $(X, ||\cdot||)$ be a and let $Y \subset X$ be a . Then we call the $X / Y$ endowed with the $||[\cdot]||$ . Remarks The requirement that $Y$ is is very important. See......

11/7/2022

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