Infinite Representability of Schrödinger Operators with Ergodic Potential
Harald EnglischUniversität Leipzig, Germany
Klaus-Detlef KürstenUniversität Leipzig, Germany
Analogous to the notion of finite representability in the theory of Banach spaces, the notions of the representability and the infinite representability of self-adjoint operators are introduced. It is proved that the infinite representability of the operator in yields that the essential spectrum of contains the spectrum of . This result applied to ergodic Schrödinger operators yields a new proof for the nonrandomness of the spectrum and for the connection between the spectrum and the density of states. A formula for the spectrum of the Hamiltonian of a substitutional alloy is presented, which clarifies the bowing effect. Similar results were found independcntly by Kirsch and Martinelli.
Cite this article
Harald Englisch, Klaus-Detlef Kürsten, Infinite Representability of Schrödinger Operators with Ergodic Potential. Z. Anal. Anwend. 3 (1984), no. 4, pp. 357–366DOI 10.4171/ZAA/113