Does there exist non-trivial linear functional on $(C[0,1], ||\cdot||_2)$ which doesn't come from the inner product on $L^2[0,1]$?
10907
Necessity of completeness of the inner product space in Riesz representation theorem
14516
The space of continuous functions $C([0,1])$ is not complete in the $L^2$ norm
87940
Question about bilinear form on Hilbert space
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
154628
What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?
25953
Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
114510
Inner Product Spaces
28888
The functional $I[w] = \int_U \frac{1}{2} |Dw|^2 - fw \, dx$ is weakly lower semicontinuous
119671
Is there an infinite dimensional $V$ such that every linear operator on $V$ is a direct sum of a nilpotent and  an invertible operator?
53528
If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
84318
A problem with the functional $F(\chi) = \int_{\mathbb{R}}(\chi'^2+\chi^2(1-\chi)^2)dx$.
39334
Non-degenerate bilinear forms and invertible matrices
89089
Prove that there is a unique inner product on $V$
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
118564
Dual cone of a $L^1$ norm cone?
63516
$C^1[0,1]$ is not complete with respect to sup norm
38761
Is the $ L^{p}$$[0,1]$ norm continuous in p?