The purpose of this note is to provide a quick survey, with no technical detail, of some of the current work on a challenging, possibly important, and certainly difficult part of functional analysis. The basic objects of the theory are operators (bounded linear transformations) on a complex Hilbert space ℋ of dimension ℵ0. (From the present point of view, both the small and the large extremes, i.e., both finite-dimensional and non-separable spaces, play trivial roles.) A subspace (closed linear manifold) ℳ of ℋ is invariant under an operator A in case A ℳ⊂ℳ. The purpose of the theory is to discuss the structure of invariant subspaces.


Invariant Subspace Toeplitz Operator Transitive Operator Unilateral Shift Quasinilpotent Operator 
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Copyright information

© Springer Basel AG 1969

Authors and Affiliations

  • P. R. Halmos
    • 1
    • 2
  1. 1.University of MichiganUSA
  2. 2.University of HawaiiUSA

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