ALMOST ISOMETRIC IDEALS IN BANACH SPACES

ALMOST ISOMETRIC IDEALS IN BANACH SPACES

A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property. Lindenstrauss spaces are known to be the class of Banach spaces t...

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Veröffentlicht in:Glasgow mathematical journal 2014-05, Vol.56 (2), p.395-407
Hauptverfasser: ABRAHAMSEN, TROND A., LIMA, VEGARD, NYGAARD, OLAV
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Banach spaces
Mathematical analysis
Subspaces
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Zusammenfassung:A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property. Lindenstrauss spaces are known to be the class of Banach spaces that are ideals in every superspace; we show that being an almost isometric ideal in every superspace characterizes the class of Gurariy spaces.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089513000335