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Spectral decomposition with monotonic spectral resolvents


Authors: I. Erdélyi and Sheng Wang Wang
Journal: Trans. Amer. Math. Soc. 277 (1983), 851-859
MSC: Primary 47A10; Secondary 47A15
MathSciNet review: 694393
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Abstract: The spectral decomposition problem of a Banach space over the complex field entails two kinds of constructive elements: (1) the open sets of the field and (2) the invariant subspaces (under a given linear operator) of the Banach space. The correlation between these two structures, in the framework of a spectral decomposition, is the spectral resolvent concept. Special properties of the spectral resolvent determine special types of spectral decompositions. In this paper, we obtain conditions for a spectral resolvent to have various monotonic properties.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0694393-2
Article copyright: © Copyright 1983 American Mathematical Society