Characteristic properties of the Gurariy space

V. P. Fonf, P. Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The Gurariy space G is defined by the property that for every pair of finite dimensional Banach spaces L ⊂ M, every isometry T: L → G admits an extension to an isomorphism (Formula presented). We investigate the question when we can take T to be also an isometry (i.e., ∈ = 0). We identify a natural class of pairs L ⊂ M such that the above property for this class with ∈ = 0 characterises the Gurariy space among all separable Banach spaces. We also show that the Gurariy space G is the only Lindenstrauss space such that its finite-dimensional smooth subspaces are dense in all subspaces.

Original languageEnglish
Pages (from-to)109-140
Number of pages32
JournalIsrael Journal of Mathematics
Volume203
Issue number1
DOIs
StatePublished - 1 Oct 2014

ASJC Scopus subject areas

  • Mathematics (all)

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