Remarks on Gurari? spaces

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00391362" target="_blank" >RIV/67985840:_____/11:00391362 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Remarks on Gurari? spaces

Original language description

We present selected known results and some new observations, involving Gurari spaces. A Banach space is Gurari 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 Gurari space. There exists a unique (up to isometry) separable Gurari space, however strong Gurari spaces cannot be separable. The structure of the class of non-separable Gurari spaces seems to be not very well understood. We discuss some of their properties and state some open questions. In articular, we characterize nonseparable Gurari spaces in terms of skeletons of separable subspaces, we construct a nonseparable Gurari space with a projectional resolution of the identity and we show that no strong Gurari space can be weakly Lindelöf determined.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2011

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Extracta Mathematicae

ISSN

0213-8743

e-ISSN

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Volume of the periodical

26

Issue of the periodical within the volume

2

Country of publishing house

ES - SPAIN

Number of pages

35

Pages from-to

235-269

UT code for WoS article

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EID of the result in the Scopus database

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