Operator Spaces Containing c0 OR l∞

J. Bonet*, P. Domański, M. Lindström, M. S. Ramanujan

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

9 Citations (Scopus)

Abstract

Let E, F be either Fréchet or complete DF-spaces and let A(E, F) ⊆ B(E, F) be spaces of operators. Under some quite general assumptions we show that: (i) A(E, F) contains a copy of c0 if and only if it contains a copy of l; (ii) if c0 ⊆ A(E, F), then A(E, F) is complemented in B(E, F) if and only if A(E, F) = B(E, F); (iii) if E or F has an unconditional basis and A(E, F) ≠ L(E, F), then A(E, F) ⊇ c0. The above results cover cases of many clssical operator spaces A. We show also that EεF contains l if and only if E or F contains l.

Original languageEnglish
Pages (from-to)250-269
Number of pages20
JournalResults in Mathematics
Volume28
Issue number3
DOIs
Publication statusPublished - Nov 1995
MoE publication typeA1 Journal article-refereed

Keywords

  • 46A04
  • 46A11
  • 46A32
  • 46A45
  • c
  • Fréchet spaces
  • l
  • Montel operators
  • reflexive operators
  • uncomplemented subspaces

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