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On a Connection Between the Numerical Range and Spectrum of an Operator on a Hilbert Space
Author(s) -
Sims Brailey
Publication year - 1974
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/jlms/s2-8.1.57
Subject(s) - connection (principal bundle) , new england , operator (biology) , hilbert space , space (punctuation) , citation , spectrum (functional analysis) , range (aeronautics) , computer science , mathematics , library science , pure mathematics , physics , quantum mechanics , engineering , law , political science , geometry , biochemistry , chemistry , repressor , politics , transcription factor , gene , aerospace engineering , operating system
is the nunzerical radius of T. W ( T ) is a convex subset of the complex plane whose closure contains the spectrum of T, u (T) . The set of eigenvalues of T is denoted by -, pa(T) and the set of approximate eigenvalues by na(T). Co a ( T ) is the convex hull of a ( T ) . A point I E W-(T) is a bare point of W(T) if I lies on the perimeter of a closed circular disc containing W(T). We say WTT) has a corner with uertex if i. E W(T) and -w(T) is contained in a half-cone with vertex J. and angle less than n. We aim to relate the vertices of corners of WTT) to points in a ( T ) . The starting point is the following lemma first suggested to me by A. M. Sinclair.