The first Szegö limit theorem for non-selfadjoint operators in the Følner algebra | Zendy

Albrecht Böttcher | Zendy; Peter Otte | Zendy

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The 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.

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