Index of notation/L

Expression		Status	Meanings	See also
$L$ (Linear Algebra)	$L(V,W)$	current	Set of all linear maps, $(:V\rightarrow W)$ - is a vector space in own right. Both vec spaces need to be over the same field, say $\mathbb{F}$.
	$L(V)$	current	Shorthand for $L(V,V)$ - see above
	$L(V,\mathbb{F})$	current	Space of all linear functionals, ie linear maps of the form $(:V\rightarrow\mathbb{F})$ as every field is a vector space, this is no different to $L(V,W)$. See - Dual vector space, written $V^*$
	$L(V_1,\ldots,V_k;W)$	current	All multilinear maps of the form $(:V_1\times\cdots\times V_k\rightarrow W)$
	$L(V_1,\ldots,V_k;\mathbb{F})$	current	Special case of $L(V_1,\ldots,V_k;W)$ as every field is a vector space. Has relations to the tensor product
	$\mathcal{L}(\cdots)$	current	Same as version above, with requirement that the maps be continuous, requires the vector spaces to be normed spaces (which is where the metric comes from to yield a topology for continuity to make sense)
$L$ (Measure Theory / Functional Analysis)	$L^p$	current	TODO: todo
	$\ell^p$	current	Special case of $L^p$ on $\mathbb{N}$