Spectral-free methods in the theory of hereditarily indecomposable Banach spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F20%3A10465529" target="_blank" >RIV/00216208:11210/20:10465529 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5HNrix4uab" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5HNrix4uab</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.36045/j.bbms.200123" target="_blank" >10.36045/j.bbms.200123</a>
Alternative languages
Result language
angličtina
Original language name
Spectral-free methods in the theory of hereditarily indecomposable Banach spaces
Original language description
We give new and simple proofs of some classical properties of hereditarily indecomposable Banach spaces, including the result by W. T. Gowers and B. Maurey that a hereditarily indecomposable Banach space cannot be isomorphic to a proper subspace of itself. These proofs do not make use of spectral theory and therefore, they work in real spaces as well as in complex spaces. We use our method to prove some new results. For example, we give a quantitative version of the latter result by Gowers and Maurey and deduce that Banach spaces that are isometric to all of their subspaces should have an unconditional basis with unconditional constant arbitrarily close to 1. We also study the homotopy relation between into isomorphisms from hereditarily indecomposable spaces.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology
Result continuities
Project
<a href="/en/project/GF17-33849L" target="_blank" >GF17-33849L: Filters, Ultrafilters and Connections with Forcing</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Bulletin of the Belgian Mathematical Society - Simon Stevin
ISSN
1370-1444
e-ISSN
2034-1970
Volume of the periodical
27
Issue of the periodical within the volume
5
Country of publishing house
BE - BELGIUM
Number of pages
13
Pages from-to
775-787
UT code for WoS article
000603431000008
EID of the result in the Scopus database
2-s2.0-85098129411