Spectral decomposition with monotonic spectral resolvents

Erdélyi, I.; Wang, Sheng Wang

doi:10.1090/S0002-9947-1983-0694393-2

Spectral decomposition with monotonic spectral resolvents
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by I. Erdélyi and Sheng Wang Wang PDF

Trans. Amer. Math. Soc. 277 (1983), 851-859 Request permission

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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