Open AccessThe first Szegö limit theorem for non-selfadjoint operators in the Følner algebra
Author(s) -
Albrecht Böttcher,
Peter Otte
Publication year - 2005
Publication title -
mathematica scandinavica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.553
H-Index - 30
eISSN - 1903-1807
pISSN - 0025-5521
DOI - 10.7146/math.scand.a-14967
Subject(s) - mathematics , trace (psycholinguistics) , operator (biology) , sequence (biology) , mathematical proof , order (exchange) , zero (linguistics) , limit (mathematics) , algebra over a field , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , geometry , chemistry , philosophy , linguistics , biochemistry , finance , repressor , transcription factor , economics , gene
We determine the first order asymptotics of the trace of $f(P_nUP_n)$ and the determinant $\det P_nUP_n$ for operators $U$ belonging to the Følner algebra associated with the sequence $\{P_n\}$ and satisfying an "index zero" condition. We present three different proofs of the main result in the case where $U$ is a normal operator.