3 problems

Let $E$ be a closed subset of the unit circle $\mathbb{T}$ of Lebesgue measure zero. A Hilbert-space contraction is a contraction acting on a Hilbert space, and $T$ is unitary when…

Let $\mathfrak g$ be a semisimple Lie algebra and let $\vartheta$ be a periodic automorphism of order $m$, inducing the grading … Let $\mathfrak g_{(0)}$ be the contraction of…

Let $1<p<\infty$ with $p\ne 2$, let $\Omega$ be a measure space, and let $T$ be a contraction on $L^p(\Omega)$. Let $S$ be the right shift on $\ell^p$, defined by … For a complex p…