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Essentially Spectral Operators
Author(s) -
Davidson Kenneth R.
Publication year - 1983
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-46.3.547
Subject(s) - mathematics , operator (biology) , quasinormal operator , compact operator , spectrum (functional analysis) , shift operator , pure mathematics , finite rank operator , compact operator on hilbert space , strictly singular operator , mathematical analysis , quantum mechanics , banach space , physics , computer science , biochemistry , chemistry , repressor , transcription factor , extension (predicate logic) , gene , programming language
We define the notion of essentially spectral operator as an operator similar to an operator of the form N + Q where N is essentially normal, Q is quasinilpotent, and NQ – QN is compact. We investigate the problem of perturbing such operators by a compact operator to obtain a spectral operator. We show that in addition to certain index obstructions related to the Brown‐Douglas‐Fillmore theory, there are also some other obstructions depending on the difference between biquasitriangularity and quasidiagonality.