JournalsjncgVol. 13, No. 4pp. 1359–1380

Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example

  • Hideki Inoue

    Nagoya University, Japan
  • Serge Richard

    Nagoya University, Japan
Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example cover
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Abstract

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some CC*-algebras of pseudo-differential operators with coefficients which either have limits at ±\pm \infty, or which are periodic or asymptotically periodic, or which are uniformly almost periodic. These various situations can be deduced from a single partial isometry which depends on several parameters. All computations are explicitly performed.

Cite this article

Hideki Inoue, Serge Richard, Index theorems for Fredholm, semi-Fredholm, and almost periodic operators: all in one example. J. Noncommut. Geom. 13 (2019), no. 4, pp. 1359–1380

DOI 10.4171/JNCG/349