Note on Spectra of Non-Selfadjoint Operators Over Dynamical Systems. Issue 2 (15th February 2018)

• Record Type: Journal Article
• Authors: Beckus, Siegfried; Lenz, Daniel; Lindner, Marko; Seifert, Christian
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 61:Issue 2(2018)
• Page Start: 371
• Page End: 386
• Publication Date: 2018-02-15
• Subjects: minimal dynamical system, -- pseudo-ergodicity, -- spectrum; Primary 47A10, -- 47A35, -- 47B37; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091517000086
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to pseudo-ergodic elements have the same spectrum and that this spectrum agrees with their essential spectrum. As a consequence we obtain that the spectrum is constant and agrees with the essential spectrum for all elements in the dynamical system if minimality holds.