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
    •  Universität Oldenburg, Germany
  • J. A. López Molina
    •  Universität Oldenburg, Germany
  • M. J. Rivera
    •  Universität Oldenburg, Germany

DOI: 10.1007/s006050050083

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


 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
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© Springer-Verlag Wien 2000