Index of notation/L
From Maths
Expression  Status  Meanings  See also  

[ilmath]L[/ilmath] (Linear Algebra) 
[ilmath]L(V,W)[/ilmath]  current  Set of all linear maps, [ilmath](:V\rightarrow W)[/ilmath]  is a vector space in own right. Both vec spaces need to be over the same field, say [ilmath]\mathbb{F} [/ilmath].  
[ilmath]L(V)[/ilmath]  current  Shorthand for [ilmath]L(V,V)[/ilmath]  see above  
[ilmath]L(V,\mathbb{F})[/ilmath]  current  Space of all linear functionals, ie linear maps of the form [ilmath](:V\rightarrow\mathbb{F})[/ilmath] as every field is a vector space, this is no different to [ilmath]L(V,W)[/ilmath].


[ilmath]L(V_1,\ldots,V_k;W)[/ilmath]  current  All multilinear maps of the form [ilmath](:V_1\times\cdots\times V_k\rightarrow W)[/ilmath]  
[ilmath]L(V_1,\ldots,V_k;\mathbb{F})[/ilmath]  current  Special case of [ilmath]L(V_1,\ldots,V_k;W)[/ilmath] as every field is a vector space. Has relations to the tensor product  
[ilmath]\mathcal{L}(\cdots)[/ilmath]  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)  
[ilmath]L[/ilmath] (Measure Theory / Functional Analysis) 
[ilmath]L^p[/ilmath]  current  TODO: todo


[ilmath]\ell^p[/ilmath]  current  Special case of [ilmath]L^p[/ilmath] on [ilmath]\mathbb{N} [/ilmath] 