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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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