Some properties of subspace convex-cyclic operators - Ahmed, Dilan; Hama, Mudhafar F.; Wozniak, Jaroslaw; Jwamer, Karwan (Sulaimani Journal for Pure and Applied Sciences, 2020)
On a Banach space X, a bounded linear operator A is a called subspace convex-cyclic associated with W as a subspace, if the set is dense in W for a vector . In this work, we use Hahn- Banach Theorem to show that the extending linear functional preserve subspace convex-cyclic operator property. Also, the algebraic structures of subspace convex-cyclic vectors can be determined, such as the spectrum.
Keywords: convex-cyclic operator; Hahn-Banach theorem; convex-cyclic spectral