Resolutions of the identity in Fréchet spaces (Q5945060)
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scientific article; zbMATH DE number 1655973
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Resolutions of the identity in Fréchet spaces |
scientific article; zbMATH DE number 1655973 |
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Resolutions of the identity in Fréchet spaces (English)
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15 October 2002
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The author proves that every \(\sigma\)-complete Boolean algebra of projections in a separable Banach space coincides with the resolution of the identity of some (continuous) scalar-type spectral operator having spectrum a compact subset of \(\Re\). He thus extends the corresponding classical result which asserts the validity of the result in the setting of a separable Hilbert space.
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\(\sigma\)-complete Boolean algebra of projections
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separable Banach space
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resolution of the identity
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scalar-type spectral operator
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