We consider the class II of contracting operators T with spectrum on the unit circle r, acting on a separable Hilbert space and subject to the following restriction on the growth of the resolvent RT(λ):
We study the spectral subspaces ΩT(B) for T∈Π, corresponding to arbitrary Borel subsets of the circle r; in parallel we study a Borel measure ωT(B) on r, adequate for ΩT(B) in the following sense:
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Ginzburg, Y.P. Spectral measures and duality of spectral subspaces of contractions with slowly growing resolvent. J Math Sci 34, 2144–2146 (1986). https://doi.org/10.1007/BF01741589
- Hilbert Space
- Unit Circle
- Spectral Measure
- Borel Measure
- Separable Hilbert Space