Integral Equations and Operator Theory

, Volume 9, Issue 3, pp 305–324

A note on the spectral theorem

  • C. Burnap
  • P. F. Zweifel

DOI: 10.1007/BF01199348

Cite this article as:
Burnap, C. & Zweifel, P.F. Integr equ oper theory (1986) 9: 305. doi:10.1007/BF01199348


We give necessary and sufficient conditions to prove a spectral theorem and a functional calculus for certain nonselfadjoint operators, H. Our method is non-perturbative: the conditions are given in terms of the resolvent (z-H)−1. We give an example of an operator satisfying these conditions. This operator is not a spectral operator of scalar type. Its spectral projections are unbounded operators defined on a common dense domainD.

Copyright information

© Birkhäuser Verlag 1986

Authors and Affiliations

  • C. Burnap
    • 1
  • P. F. Zweifel
    • 2
  1. 1.Department of MathematicsUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Center for Transport Theory and Mathematical PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA