On almost isometric ideals in Banach spaces

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• 作者：T. S. S. R. K. Rao
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：181
• 期：1
• 页码：169-176
• 全文大小：376 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：181

文摘

In this note we study the notion of almost isometric ideals recently introduced in Abrahamsen et al. (Glasg Math J 56:395–407, 2014) for separable Banach spaces. We show that a closed subspace of the Gurariy space that is an almost isometric ideal is itself the Gurariy space. In this space we show that all infinite dimensional M-ideals are almost isometric ideals. In \(c_0\) we show that any finite codimensional proximinal ideal is an almost isometric ideal. We solve in the negative the 3-space problem for almost isometric ideals. We also give an example to show that being an almost isomeric ideal is not preserved by spaces of vector-valued continuous functions on a compact set. We show that any separable \(L^1\)-predual space with a non-separable dual, has an ideal that is not an almost isometric ideal. We also study properties of almost isometric ideals that are hyperplanes.KeywordsAlmost isometric idealsExtension of isometries\(L^1\)-predual spacesSeparable spacesGurariy space