Index of norms and absolute values

This index is for:

• $\Vert\cdot\Vert$-like (which are norms) and
• $\vert\cdot\vert$-like (which are absolute values)

expressions

Norms

Expression		Index	Context	Details
$$\|\cdot\|$$	$$\|v\|$$		Functional Analysis Real Analysis	Denotes the Norm of a vector
$$\|\cdot\|_{C^k}$$	$$\|f\|_{C^k}$$	CK	Functional Analysis	This Norm is defined by $$\|f\|_{C^k}=\sum^k_{i=0}\sup_{t\in[0,1]}(|f^{(i)}(t)|)$$ - note $$f^{(i)}$$ is the $$i^\text{th}$$ derivative.
$$\|\cdot\|_\infty$$	$$\|f\|_\infty$$	INFINITY	Functional Analysis Real Analysis	It is a norm on $$C([a,b],\mathbb{R})$$ , given by $$\|f\|_\infty=\sup_{x\in[a,b]}(|f(x)|)$$
$$\|\cdot\|_{L^p}$$	$$\|f\|_{L^p}$$	LP	Functional Analysis	$$\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}$$ - it is a Norm on $$\mathcal{C}([0,1],\mathbb{R})$$

Absolute values

Expression		Index	Context	Details
$$|\cdot|$$	$$|x|$$		Real analysis Abstract algebra	The traditional Absolute value