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On the Trace Formula of Perturbation Theory. II
Author(s) -
Jonas Peter
Publication year - 1999
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.19991970104
Subject(s) - mathematics , trace class , hilbert space , unitary state , integrable system , pure mathematics , function space , spectral theory , nuclear operator , class (philosophy) , space (punctuation) , square integrable function , perturbation (astronomy) , trace (psycholinguistics) , spectral space , mathematical analysis , quantum mechanics , banach space , finite rank operator , linguistics , artificial intelligence , political science , computer science , law , philosophy , physics
Abstract In a previous paper for a class of pairs of operators in a Hilbert space with nuclear difference or under a more general nuclearity condition there was introduced a spectral shift functional. Here we consider the local integrability of this spectral shift functional, i.e., the problem when this functional can locally be represented by an integrable function. The general results are then applied to pairs of definitizable and locally definitizable unitary operators in a Krein space.