We study the following question: suppose that A and ℬ are two algebras of complex n × n matrices such that the ring commutator [A, B] = AB – BA is "small" for each A ∈ A and B ∈ ℬ; does this imply ...

Let ω be a weight on ℤ, and assume that the translation operator S : (un)n∈ℤ → (un–1)n∈ℤ is bounded on ${\mathrm{\ell}}_{\mathrm{\omega }}^{2}\left(\mathrm{\mathbb{Z}}\right)$, and that the spectrum ...