Abstract
1. In this note we shall answer in the negative the following question posed by L.A. Fialkow in [3, p. 227]. Let U be a (linear, bounded) operator acting on the (complex) Hilbert space K ,and let us assume that σ(U) = σ 1 U σ 2 is a non-trivial decomposition of the spectrum σ(U) of U into the union of two disjoint closed sets. For j = 1,2,let K(σ 1,U) denote the spectral subspace obtained by the Riesz-Dunford functional calculus. It is well-known that K splits into the direct sum of the hyperivariant subspaces K(σ 1,U) and K(σ 2): K = K(σ 1,U + K(σ 2,U).
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References
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Dedicated to Professor I. Gohberg on the occasion of his 60th birthday
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© 1989 Birkhäuser Verlag Basel
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Kérchy, L. (1989). On the Inclination of Hyperinvariant Subspaces of C11-Contractions. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40/41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9144-8_35
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DOI: https://doi.org/10.1007/978-3-0348-9144-8_35
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