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Israel Journal of Mathematics

, 169:221 | Cite as

Classes of strictly singular operators and their products

  • G. Androulakis
  • P. Dodos
  • G. Sirotkin
  • V. G. Troitsky
Article

Abstract

V. D. Milman proved in [20] that the product of two strictly singular operators on L p [0, 1] (1 ⩽ p < 1) or on C[0, 1] is compact. In this note we utilize Schreier families \( \mathcal{S}_\xi \) in order to define the class of \( \mathcal{S}_\xi \)-strictly singular operators, and then we refine the technique of Milman to show that certain products of operators from this class are compact, under the assumption that the underlying Banach space has finitely many equivalence classes of Schreier-spreading sequences. Finally we define the class of \( \mathcal{S}_\xi \)-hereditarily indecomposable Banach spaces and we examine the operators on them.

Keywords

Banach Space Dimensional Subspace Basic Sequence Separable Banach Space Block Sequence 
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

© Hebrew University Magnes Press 2008

Authors and Affiliations

  • G. Androulakis
    • 1
  • P. Dodos
    • 2
  • G. Sirotkin
    • 3
  • V. G. Troitsky
    • 4
  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Department of Mathematics, Faculty of Applied SciencesNational Technical University of AthensAthensGreece
  3. 3.Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA
  4. 4.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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