Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 411, Issue 2, Pages 931-946Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2013.10.025
Keywords
Rigged Hilbert spaces; Operators; Spectrum
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A notion of resolvent set for an operator acting in a rigged Hilbert space D subset of H subset of D-x is proposed. This set depends on a family of intermediate locally convex spaces living between D and D-x, called interspaces. Some properties of the resolvent set and of the corresponding multivalued resolvent function are derived and some examples are discussed. (C) 2013 Elsevier Inc. All rights reserved.
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