10 Multiplicative Representations of Resolvents

  • Michael I. Gil’
Part of the Lecture Notes in Mathematics book series (LNM, volume 1830)


In the present chapter we introduce the notion of the multiplicative operator integral in a separable Hilbert space H. By virtue of the multiplicative operator integral, we derive spectral representations for resolvents of various classes of P-triangular operators. These representations are generalizations of the classical spectral representation for the resolvent of a normal operator. If the maximal resolution of the identity is discrete, then the multiplicative integral is an operator product.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michael I. Gil’
    • 1
  1. 1.Department of MathematicsBen Gurion University of NegevBeer-ShevaIsrael

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