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ALMOST ISOMETRIC IDEALS IN BANACH SPACES

Published online by Cambridge University Press:  13 August 2013

TROND A. ABRAHAMSEN ,
VEGARD LIMA  and
OLAV NYGAARD
TROND A. ABRAHAMSEN
Affiliation:
Department of Mathematics, Agder University, Servicebox 422, 4604 Kristiansand, Norway e-mail: Trond.A.Abrahamsen@uia.no
VEGARD LIMA
Affiliation:
Ålesund University College, Postboks 1517, 6025 Ålesund, Norway e-mail: Vegard.Lima@gmail.com
OLAV NYGAARD
Affiliation:
Department of Mathematics, Agder University, Servicebox 422, 4604 Kristiansand, Norway. e-mail: Olav.Nygaard@uia.no
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Abstract

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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.

Keywords

46B2046B04
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 395 - 407
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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