Invariant subspaces for tridiagonal operators.
In this paper, the author obtains a non-trivial invariant closed subspace for a ``tridiagonal operator'' on a Banach space of complex sequences indexed by the natural numbers \(\mathbb{N}\) with the canonical basis \((\delta_{n})_{n \geq 1}\). It extends a result of \textit{A. Atzmon} who proved in [J. Funct. Anal. 178, 372--380 (2000; Zbl 0978.47022)] that every bishift on a sequence space has a nontrivial invariant subspace.
scientific article; zbMATH DE number 1886877