The structure of almost-invariant half-spaces for some operators

@inproceedings{Sirotkin2014TheSO,
  title={The structure of almost-invariant half-spaces for some operators},
  author={Gleb Sirotkin and Ben Wallis},
  year={2014}
}
Abstract Given a Banach space X and an operator T ∈ L ( X ) , an almost-invariant half-space (AIHS) is a closed subspace Y satisfying T Y ⊆ Y + F for some finite-dimensional subspace F and dim ⁡ ( Y ) = dim ⁡ ( X / Y ) = ∞ . In this paper we study the connection between AIHS and noncompactness of some subsets of the unit ball, chains of T -invariant subspaces, and different parts of spectrum of T and T ⁎ . We describe a simple template for such subspaces and show that if T is quasinilpotent or… CONTINUE READING