Consider the normed linear space $R^2$ equipped with the norm given by $||(x,y)||=|x|+|y|$ and the subspace $X=\{(x,y)\in R^2 : x=y\}.$ Let $f(x,y)=3x$ on $X$. Then what is the Hahn Banach extension of $f$.?
I have gone through different books and dufferent methods and idea of how to find such extensions. But stil not comfortable with it. Could you please help me understand a general method? Is there any general idea? Is the norm of $f \ 3?$. A similar question is there in one book but there norm of $f$ is $\frac{1}{\sqrt 5}$.