Open AccessOn Essential Selfadjointness, Distinguished Selfadjoint Extension and Essential Spectrum of Dirac Operators with Matrix Valued Potentials
Author(s) -
Masaharu Arai
Publication year - 1983
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195182974
Subject(s) - mathematics , norm (philosophy) , bounded function , identity matrix , operator norm , operator (biology) , bounded operator , essential spectrum , hilbert space , pure mathematics , dirac operator , spectrum (functional analysis) , matrix (chemical analysis) , inner product space , mathematical analysis , eigenvalues and eigenvectors , chemistry , quantum mechanics , physics , chromatography , biochemistry , repressor , political science , transcription factor , law , gene
(1.2) ajak+akaj=2djkl (/, fe = l, 2, 3, 4). We denote by HQ the operator H with We denote by and | | the usual inner product and norm in C, respectively, and by ( , ) and || || the inner product and norm in the Hilbert space «#=[L2CR )II, respectively. We also denote by | | and || || the operator norm of a 4x4 matrix and a bounded linear operator in «#, respectively. We denote by / the 4x4 identity matrix, which at times implies the 2x2 identity matrix, but no confusion will occur. For a closable operator T in JC, we denote by T its closure. For an (formal) operator T, we denote by T the restriction of T to the domain
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