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Abstract

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.

Keywords

Invariant Subspace Toeplitz Operator Transitive Operator Unilateral Shift Quasinilpotent Operator 
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 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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