@article{2da051cc7176457fa401a3000dcd456f,

title = "Characteristic properties of the Gurariy space",

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.",

author = "Fonf, {V. P.} and P. Wojtaszczyk",

note = "Funding Information: ∗Both authors were partially supported by the Foundation for Polish Science. The first-named author was partially supported by the Israel Science Founda-tion, Grant 209/09 and by European Grant Spade 2. The second-named author was partially supported by the Center for Advanced Studies in Mathematics of Ben-Gurion University of the Negev, the “HPC Infrastructure for Grand Chal-lenges of Science and Engineering Project, co-financed by the European Regional Development Fund under the Innovative Economy Operational Programme and Polish NCN grant DEC2011/03/B/ST1/04902. Publisher Copyright: {\textcopyright} 2014, Hebrew University Magnes Press.",

year = "2014",

month = oct,

day = "1",

doi = "10.1007/s11856-014-0016-4",

language = "English",

volume = "203",

pages = "109--140",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "1",

}