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The Point Spectrum of Unitary Dilations in Kreĭ Spaces
Author(s) -
Temme Dirk
Publication year - 1998
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.19981940114
Subject(s) - mathematics , eigenvalues and eigenvectors , unitary state , dilation (metric space) , pure mathematics , spectrum (functional analysis) , unit circle , point (geometry) , mathematical analysis , combinatorics , geometry , quantum mechanics , physics , political science , law
For a bicontractive operator T on a Kreĭ space the connections between its eigenvalues and eigenstructure and the eigenvalues and eigenstructure of its minimal unitary dilation U are studied. For eigenvalues on the unit circle of T in general only part of the eigenspace of T will return its an eigenspace of U and the corresponding eigenvalue will be a singular critical point of U .