When are integral operators trace class?

by keej   Last Updated May 11, 2017 01:20 AM - source

Define an integral operator $T$ on $L^2([0,1])$ by $$Tf(x) = \int\int K(x, y) f(y) \, dx\, dy$$. Such an operator is Hilbert-Schmidt when $K$ is in $L^2([0,1]\times [0,1])$.

I heard that if $K$ is smooth, then $T$ is in fact trace-class. Why is this?

When is such an operator trace-class?



Related Questions



Find Volume of $V_{2}(a,b)$

Updated January 08, 2019 00:20 AM


Norm of an integral operator $L^1 \to L^\infty$

Updated August 08, 2015 15:08 PM