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The Spectral Shift Function for Certain Block Operator Matrices
Author(s) -
Adamjan Vadim,
Langer Heinz
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200003)211:1<5::aid-mana5>3.0.co;2-u
Subject(s) - mathematics , operator matrix , diagonal , operator (biology) , spectrum (functional analysis) , sign (mathematics) , trace (psycholinguistics) , function (biology) , block (permutation group theory) , trace class , matrix (chemical analysis) , class (philosophy) , constant (computer programming) , pure mathematics , shift operator , combinatorics , mathematical analysis , compact operator , hilbert space , geometry , physics , extension (predicate logic) , quantum mechanics , computer science , philosophy , materials science , repressor , artificial intelligence , linguistics , chemistry , composite material , biology , biochemistry , evolutionary biology , transcription factor , programming language , gene
Let L 0 be a 2 × 2 diagonal self‐adjoint block operator matrix with entries A and D . If operators B and B * are added to the off diagonal zeros, certain parts of the spectrum of L 0 move to the right and other parts move to the left. In this paper it is shown that, correspondingly, if B is a trace class operator M. G. Krein's spectral shift function is of constant sign on certain intervals.