Bounded Operators

Part of the Universitext book series (UTX)


We have shown that most of the theorems on triangularizability of operators on finite-dimensional spaces have satisfactory extensions to collections of compact operators. However, we shall see that there are few generalizations to collections of arbitrary bounded operators: There are counterexamples to most reasonable conjectures. In particular, there are commutative sets of operators that are irreducible, and there are irreducible algebras of nilpotent operators, and irreducible semigroups consisting of nilpotent operators of index two. There are also some affirmative results. There are many cases in which pairs of operators whose commutator has rank one are triangularizable, although there are counterexamples to the general extension of Laffey’s Theorem. There is a similar situation with respect to nonnegative operators and for bands.


Banach Space Bound Operator Invariant Subspace Compact Operator Banach Lattice 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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