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Geometrical and Spectral Properties of Dilations

  • Béla Sz.-Nagy
  • Hari BercoviciEmail author
  • Ciprian Foias
  • László Kérchy
Chapter
  • 1.9k Downloads
Part of the Universitext book series (UTX)

Abstract

In the sequelwe consider a contraction T on the real or complex Hilbert space \(\mathfrak{H}\), and its minimal unitary dilation U on the Hilbert space \(\mathfrak{K}\), real or complex, respectively \(\left( {\mathfrak{K}\supset\mathfrak{H}} \right)\). The linear manifolds
$$\begin{array}{*{20}c}{\mathfrak{L_0} = \left( {U - T} \right)\mathfrak{H}} & {{\rm and}} & {\begin{array}{*{20}c}{\mathfrak{L^*_0} = \left( {U - T^*} \right)\mathfrak{H}} \hfill & {\left( {\subset\mathfrak{K}} \right)}\hfill \\\end{array}} \hfill\\\end{array}$$
(1.1)
and their closures
$$\begin{array}{*{20}c} {\mathfrak{L} = \overline{\left( {U - T} \right)\mathfrak{H}},} \hfill & {\mathfrak{L^*} = \overline{\left( {U^* - T^*} \right)\mathfrak{H}}} \hfill \\ \end{array}$$
(1.2)
play an important role in our investigations.

Keywords

Interpolation Problem Complex Hilbert Space Linear Manifold Residual Part Spectral Multiplicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Béla Sz.-Nagy
  • Hari Bercovici
    • 1
    Email author
  • Ciprian Foias
    • 2
  • László Kérchy
    • 3
  1. 1.Mathematics DepartmentIndiana UniversityBloomingtonUSA
  2. 2.Mathematics DepartmentTexas A & M UniversityCollege StationUSA
  3. 3.Bolyai InstituteSzeged UniversitySzegedHungary

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