Infinite Representability of Schrödinger Operators with Ergodic Potential

  • Harald Englisch

    Universität Leipzig, Germany
  • Klaus-Detlef Kürsten

    Universität 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 AA in BB yields that the essential spectrum of BB contains the spectrum of AA. 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. 357–366

DOI 10.4171/ZAA/113