New posts in Functional Analysis

If $f \in C[a,b]$ has $\int_{a}^{b}f(x)x^{n}dx=0$ for all $n\in \mathbb{N}$, then $f=0$.

Is the identity functor naturally isomorphic to a covariant dual functor?

Understanding the proof $C(X)$ is complete

Is $0$ the only vector in the kernel of every bounded linear functional?

Hölder norm of the Hilbert Transform

I want to prove that two norms are equivalent but I am struggling with an upper bound

Proving James' Theorem

If $Y\subset X$ are Banach spaces such that $Y$ is dense in $X$, is it true that $X'$ is dense in $Y'$?

Show that the carré du champ operator is nonnegative

Norm in Sequence Space such that Convergence in Norm does not imply Pointwise Convergence