Finite dimensional approximations of operators related to groups and their applications

• Autores: Jan Paul Boschheidgen
• Directores de la Tesis: Andrei Jaikin-Zapirain (dir. tes.)
• Lectura: En la Universidad Autónoma de Madrid ( España ) en 2023
• Idioma: inglés
• Número de páginas: 142
• Tribunal Calificador de la Tesis: Steffen Kionke (presid.) , Yago Antolín Pichel (secret.) , Holger Kammeyer (voc.)
• Enlaces
  • Tesis en acceso abierto en: Biblos-e Archivo
• Resumen

  • In the first part we show a generalization of the effective Luck approximation property. We show that there exists a function that bound the spectral concentration of all matrices that appear as representations from an algebraic operator.

    In the second part we answer a question posed by Wolfgang Luck. We show that the von Neumann rank function and the von Neumann rank function twisted with a finite dimensional representation only differ by a factor.

    In the last part we show shat in general the Brown measure of an Operator from a group ring can not be approximated using finite quotients. We give an explicit counterexample.