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 ...

Suppose H is a complex Hilbert space and T ∈ L(H) is a bounded operator. For each closed set F $\subset$ C let HT(F) denote the corresponding spectral manifold. Let σloc(T) denote the set of all ...

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 ...

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 ...

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 ...

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 ...