- #1
yifli
- 70
- 0
Homework Statement
show that if [tex]V=M \oplus N[/tex], then [tex]V^*=M^o+N^o[/tex]
2. The attempt at a solution
So I need to prove for any [tex]f \in V*[/tex], [tex]f(\epsilon)=(g+h)(\epsilon)[/tex], where [tex]g\in M^o[/tex] and [tex]h\in N^o[/tex].
[tex](g+h)(\epsilon)=g(\epsilon)+h(\epsilon)=g(\alpha+\beta)+h(\alpha+\beta)=g(\beta)+h(\alpha)[/tex], where[tex]\alpha \in M[/tex] and [tex]\beta \in N[/tex].
I'm stuck here, how to proceed?
Thanks