All Questions

Rudin's book contains in chapter 10 a spectral mapping theorem for (self-adjoint) unbounded operators that respects the point-spectrum, in the sense that he shows $f(\sigma_p(T))=\sigma_p(f(T))$ for ...

In a paper I am currently reading, the author uses that if $T$ is an operator given by the kernel $$T(x,y) = \int_{\mathbb R} p(x,z) q(z,y) dz,$$ then $$\lvert \operatorname{tr} T \rvert \leq \lVert T ...

My question is somewhat broad, but I do not know how to precisely state the issue. I am investigating stability of certain class of scalar PDE on $\mathbb{R}$. Previous work in this topic has ...

Let $T$ be a (everywhere defined) self-adjoint operator on a complex Hilbert space $\mathcal{H}$. I am interested in results that give (non-trivial, possibly mild) sufficient conditions on $T$ to ...