We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial ...

A class of operators (which includes the unilateral weighted shifts and the noninvertible bilateral weighted shifts on Hilbert spaces), with the property that every element of the commutant of the ...

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title “On the invariant subspace problem in Hilbert spaces”. The paper is just 13 pages long and its ...

Mathematician Per Enflo, who solved a huge chunk of the 'invariant subspaces problem' decades ago, may have just finished his work. When you purchase through links on our site, we may earn an ...

The study of shift-invariant systems and abelian groups underpins several modern advances in harmonic analysis, signal processing and pure mathematics. At its core, this area explores how translation ...