New posts in Compact Operators

Calculate the operator norm of $A: L^2[0,1] \to L^2[0,1]$ defined by $(Af)(x):=i\int_0^x f(t)\,dt-\frac{i}{2} \int_0^1 f(t) \,dt$

A sufficient and necessary condition for a special linear operator to be compact

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

Showing that $0\leq A\leq B$ and $B \in \mathcal{L}_c(H)$ implies that $A \in \mathcal{L}_c(H)$.

Integral Operator in $L^2$

Example of a non-trace class operator

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

Example of a noncompact operator on $L^2([0,1])$

Convergence of $A_nT$ to $AT$ in operator norm for compact $T$

Bounded linear operator commuting with every compact operators