On spectral approximation, Følner sequences and crossed products Articles uri icon

publication date

  • June 2013

start page

  • 155

end page

  • 171

volume

  • 170

International Standard Serial Number (ISSN)

  • 0021-9045

Electronic International Standard Serial Number (EISSN)

  • 1096-0430

abstract

  • Dedicated to Paco Marcellán on his 60th birthday. Abstract: In this article we study Følner sequences for operators and mention their relation to spectral approximation problems. We construct a canonical Følner sequence for the crossed product of a discrete amenable group Gamma with a concrete C∗-algebra A with a Følner sequence. We also state a compatibility condition for the action of Gamma on A. We illustrate our results with two examples: the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C∗-algebra generated by bounded Jacobi operators. These examples can be interpreted in the context of crossed products. The crossed products considered can be also seen as a more general frame that included the set of generalized band-dominated operators.

keywords

  • spectral approximation; c∗-algebras; crossed products; følner sequences; quasidiagonality; amenable groups; rotation algebra