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Intersections of the Left and Right Essential Spectra of 2 × 2 Upper Triangular Operator Matrices
Author(s) -
Li Yuan,
Sun XiuHong,
Du HongKe
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003492
Subject(s) - mathematics , triangular matrix , spectrum (functional analysis) , essential spectrum , operator (biology) , hilbert space , operator matrix , combinatorics , matrix (chemical analysis) , pure mathematics , chemistry , physics , quantum mechanics , biochemistry , repressor , transcription factor , invertible matrix , gene , chromatography
In this paper, perturbations of the left and right essential spectra of 2 × 2 upper triangular operator matrix M C are studied, whereM C = (A C0 B)is an operator acting on the Hilbert space H ⊕ K . For given operators A and B , the sets∩ C ∈ B ( K , H )σ l e ( M C ) and∩ C ∈ B ( K , H )σ r e ( M C ) are determined, where σ le ( T ) and σ re ( T ) denote, respectively, the left essential spectrum and the right essential spectrum of an operator T . 2000 Mathematics Subject Classification 47A10, 47A55.