New posts in Lp Spaces

A proper subspace of a normed vector space has empty interior clarification

Use Fatou Lemma to show that $f$ takes real values almost everywhere.

A characterization of Weak Convergence in $L^p$ spaces

Pointwise multiplication by unbounded function throws us out of $L^2(\mu)$

If $T:L^p[0,1] \to L^p[0,1]$ bounded for $1 < p < \infty$ with continuous image, then it's compact

Are polynomials dense is L2 of the unit disk?

Using Banach-Alaoglu theorem on $L^1$

Is the rectangular function a convolution of $L^1$ functions?

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

$T: L^2[0,1] \to L^2[0,1]$, $Tf(x)= \frac{1}{x}\int_{0}^x f(y)$, is a bounded but not compact operator.