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arXiv:1212.2954 [math.FA]AbstractReferencesReviewsResources

On the essential spectrum of the sum of self-adjoint operators and the closedness of the sum of operator ranges

Ivan S. Feshchenko

Published 2012-12-12, updated 2013-06-01Version 2

We get a criterion for 0 to be in the essential spectrum of a sum of self-adjoint operators whose pairwise products are compact. Using this result, we obtain necessary and sufficient conditions for the sum of ranges of such operators to be closed.

Comments: 9 pages
Journal: Banach journal of mathematical analysis, Volume 8, issue 1, 2014
Categories: math.FA
Subjects: 47B15, 46C07
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