Year: 2011
Type: article
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 Lindelöf determined.
Authors: Garbulińska, Joanna, Kubiś, Wiesław
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Social Fund
OpenAlex ID: W1953469397