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arXiv · 1111.5840

Remarks on Gurarii spaces

Joanna Garbulińska·Wiesław Kubiś
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Abstract

We present selected known results and some of their improvements, involving Gurarii spaces. A Banach space is Gurarii if it has certain natural extension property for almost isometric embeddings of finite-dimensional spaces. Deleting the word "almost", we get the notion of a strong Gurarii space. There exists a unique (up to isometry) separable Gurarii space, however strong Gurarii spaces cannot be separable. The structure of the class of non-separable Gurarii spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In particular, we characterize non-separable Gurarii spaces in terms of skeletons of separable subspaces, we construct a non-separable Gurarii space with a projectional resolution of the identity and we show that no strong Gurarii space can be weakly Lindel\"of determined.

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Joanna Garbulińska, Wiesław Kubiś. 2011-11-24. Remarks on Gurarii spaces. https://arxiv.org/abs/1111.5840

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