Monatshefte für Mathematik

, Volume 130, Issue 1, pp 7–18

On Pitt’s Theorem for Operators between Scalar and Vector-Valued Quasi-Banach Sequence Spaces

  • A. Defant
  • J. A. López Molina
  • M. J. Rivera

DOI: 10.1007/s006050050083

Cite this article as:
Defant, A., Molina, J. & Rivera, M. Mh Math (2000) 130: 7. doi:10.1007/s006050050083
  • 52 Views

Abstract.

 We find natural conditions under which all continuous linear operators between two scalar or vector-valued quasi-Banach sequence spaces are compact. In the case of scalar-valued Banach sequence spaces we show that all such operators essentially factorize through diagonal operators between suitable \(\)-spaces.

1991 Mathematics Subject Classification: 46M0546A32
Key words: Compact operatorsPitt’s theoremquasi-Banach sequence spacesconvexityconcavity

Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • A. Defant
    • 1
  • J. A. López Molina
    • 1
  • M. J. Rivera
    • 1
  1. 1. Universität Oldenburg, GermanyDE
  2. 2. Universidad Politécnica de Valencia, SpainES