Abstract of a paper by Joanna Garbulinska and Wiesaw Kubis
This is an announcement for the paper "Remarks on Gurarii spaces" by Joanna Garbulinska and Wiesaw Kubis. 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. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B20 Remarks: 30 pages Submitted from: kubis@math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1111.5840 or http://arXiv.org/abs/1111.5840
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alspach@math.okstate.edu