caa a22 4500 445884495 CHVBK 20180317145555.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10711-010-9491-x doi (NATIONALLICENCE)springer-10.1007/s10711-010-9491-x A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states [Elektronische Daten] [Daniel Lenz, Fabian Schwarzenberger, Ivan Veselić] In this paper we consider bounded operators on infinite graphs, in particular Cayley graphs of amenable groups. The operators satisfy an equivariance condition which is formulated in terms of a colouring of the vertex set of the underlying graph. In this setting it is natural to expect that the integrated density of states (IDS), or spectral distribution function, exists. We show that it can be defined as the uniform limit of approximants associated to finite matrices. The proof is based on a Banach space valued ergodic theorem which even allows explicit convergence estimates. Our result applies to a variety of group structures and colouring types, in particular to periodic operators and percolation-type Hamiltonians. Springer Science+Business Media B.V., 2010 Cayley graphs nationallicence Discrete random operators nationallicence Integrated density of states nationallicence Uniform approximation nationallicence Uniform ergodic theorem nationallicence Lenz Daniel Mathematisches Institut, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany aut Schwarzenberger Fabian Emmy-Noether-Projekt, Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany aut Veselić Ivan Emmy-Noether-Projekt, Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany aut Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 1-34 0046-5755 150:1<1 2011 150 10711 https://doi.org/10.1007/s10711-010-9491-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9491-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lenz Daniel Mathematisches Institut, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany aut NATIONALLICENCE 700 1- Schwarzenberger Fabian Emmy-Noether-Projekt, Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany aut NATIONALLICENCE 700 1- Veselić Ivan Emmy-Noether-Projekt, Fakultät für Mathematik, TU Chemnitz, 09107, Chemnitz, Germany aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 150/1(2011-02-01), 1-34 0046-5755 150:1<1 2011 150 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer