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Spectrum of a Self‐Adjoint Operator and Palais–Smale Conditions
Author(s) -
Stuart C. A.
Publication year - 2000
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008455
Subject(s) - spectrum (functional analysis) , hilbert space , operator (biology) , mathematics , self adjoint operator , rayleigh quotient , quotient , pure mathematics , quasinormal operator , hermitian adjoint , quadratic equation , mathematical analysis , space (punctuation) , finite rank operator , physics , computer science , banach space , quantum mechanics , eigenvalues and eigenvectors , geometry , biochemistry , repressor , transcription factor , gene , chemistry , operating system
The spectrum and essential spectrum of a self‐adjoint operator in a real Hilbert space are characterized in terms of Palais–Smale conditions on its quadratic form and Rayleigh quotient respectively.