8 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…

Consider the de Sitter-Galilei and anti-de Sitter-Galilei algebras, together with their deformations obtained from de Sitter and anti-de Sitter deformations by quantum $c\to\infty$…

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 $f$ be a Lipschitz function on the real line, and let $A$ and $B$ be noncommuting contractions. Recall that for Lipschitz functions of two noncommuting self-adjoint operators t…

A contraction is a bounded operator $A$ with $\\|A\\|\leq 1$. For a function $f$ of three operators, write $f(A,B,C)$ for its functional calculus on a triple of contractions…

A solvable Lie algebra is a Lie algebra whose derived series terminates at zero; a semisimple Lie algebra is a Lie algebra with zero solvable radical. A contraction of a Lie algebr…

JK-invariant conjecture. The JK invariants of $\widetilde{\mathfrak g}$ coincide with those of the semisimple Lie algebra $\mathfrak g$.

Composition conjecture. Any contraction to a Lie algebra possessing nontrivial gradings is a composition of generalized Inönü–Wigner contractions.