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Spectral measures and duality of spectral subspaces of contractions with slowly growing resolvent

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Abstract

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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Literature cited

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 73, pp. 203–206, 1977.

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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

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Keywords

  • Hilbert Space
  • Unit Circle
  • Spectral Measure
  • Borel Measure
  • Separable Hilbert Space