Linear Map Form: E x R to R [SOLVED]

[quasar987]

[SOLVED] form of a linear map

Homework Statement

Say E is a linear space (not necessarily of finite dimension), and R is the real numbers. Say we have a (contiuous) linear form T from E x R to R. Can we say T is of such and such a form? Particularily, can we say that T=g1+g2 where g1:E-->R and g2:R-->R are linear forms?

 

[Dick]

Sure. Take (x,y) in ExR. Define g1(x,y)=T(x,0) and g2(x,y)=T(0,y). Is that what you meant? Doesn't that work?