Extension of operators from subspaces of c0(Γ)into C(K) spaces

W. B. Johnson, M. Zippin

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

It is shown that for every ε> 0, every bounded linear operator T from a subspace X of C0(Γ) into a C(K) space has an extension T from C0(Γ) into the C(K) space such that ||T|| ≤ (1 + ε)||T||. Even when Γis countable, T is compact, and X has codimension 1 in Cq, the “ε” cannot be replaced by 0. These results answer questions raised by J. Lindenstrauss and A. Pelczynski in 1971.

Original languageEnglish
Pages (from-to)751-754
Number of pages4
JournalProceedings of the American Mathematical Society
Volume107
Issue number3
DOIs
StatePublished - Nov 1989

Keywords

  • Continuous selections
  • Extension of operators
  • Hahn-Banach extensions
  • Operators into C(K)

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