Amalgamations of classes of Banach spaces with a monotone basis

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10335068" target="_blank" >RIV/00216208:11320/16:10335068 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.4064/sm8281-7-2016" target="_blank" >http://dx.doi.org/10.4064/sm8281-7-2016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4064/sm8281-7-2016" target="_blank" >10.4064/sm8281-7-2016</a>

Result language
angličtina
Original language name
Amalgamations of classes of Banach spaces with a monotone basis
Original language description
It was proved by Argyros and Dodos that, for many classes C of separable Banach spaces which share some property P, there exists an isomorphically universal space that satisfies P as well. We introduce a variant of their amalgamation technique which provides an isometrically universal space in the case that C consists of spaces with a monotone Schauder basis. For example, we prove that if C is a set of separable Banach spaces which is analytic with respect to the Effros Borel structure and every X is an element of C is reflexive and has a monotone Schauder basis, then there exists a separable reflexive Banach space that is isometrically universal for C.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GP14-04892P" target="_blank" >GP14-04892P: Descriptive set theory and universality questions in Banach space theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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