Verify that the Riesz vector is unique

[rhobymic]

Homework Statement

The Riesz representation theorem gives us that forall f in V* there exists a unique R_f in V such that f(x) = <x, R_f >. (<,> is my attempt to type inner product angle brackets) Verify that R_f is unique.

Homework Equations

If I knew the relevant equations I think I could get this done on my own

The Attempt at a Solution

No attempts at a solution because i don't even know where to begin.

Usually when i prove uniqueness I start with the assumption that two solutions exist and then prove that they end up being the same solution... but i don't see how to work that angle here.

Any help would be great

 

[Dick]

Homework Statement

The Riesz representation theorem gives us that forall f in V* there exists a unique R_f in V such that f(x) = <x, R_f >. (<,> is my attempt to type inner product angle brackets) Verify that R_f is unique.

Homework Equations

If I knew the relevant equations I think I could get this done on my own

The Attempt at a Solution

No attempts at a solution because i don't even know where to begin.

Usually when i prove uniqueness I start with the assumption that two solutions exist and then prove that they end up being the same solution... but i don't see how to work that angle here.

Any help would be great

You already have the correct approach. Assume there are two solutions. Write down the equations the two vectors in V would have to satisfy.