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Invertibility of 2 × 2 operator matrices
Author(s) -
Huang Junjie,
Sun Junfeng,
Chen Alatancang,
Trunk Carsten
Publication year - 2019
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/mana.201800351
Subject(s) - mathematics , invertible matrix , surjective function , operator (biology) , operator matrix , quasinormal operator , multiplication operator , finite rank operator , pure mathematics , shift operator , decomposition , compact operator , hamiltonian (control theory) , matrix (chemical analysis) , algebra over a field , hilbert space , mathematical optimization , banach space , computer science , repressor , ecology , chemistry , biology , biochemistry , transcription factor , programming language , extension (predicate logic) , gene , materials science , composite material
Properties of right invertible row operators, i.e., of 1 × 2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2 × 2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.