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Topological and geometric structures in Banach spaces

Project goals

Stability of weak Asplund spaces and Gateaux differentiability spaces, Banach spaces with projectional skeleton, stability of Valdivia compacta, topological characterizations of some classes of Banach spaces, compact convex sets - duality of compact spaces and Banach spaces and topological classification, weak topology of weakly K-analytic Banach spaces, geometric properties of boundaries of compact convex sets, strongly affine functions and Baire classes of Banach spaces, isomorphic properties of L_1-preduals, descriptive properties of ranges of derivatives on Banach spaces, descriptive properties of norm and weak topologies on Banach spaces, binormality in Banach spaces, spaces of continuous functions, renormings and differentiability, weak-star uniformly Kadec-Klee norms, Lipschitz homeomorphisms, Markushevich bases, extensions of special Lipschitz mappings, retracts, absolutely minimal Lipschitz functions, Gurarij space, compacta with extra structure

Keywords

Banach spaceweak topologyweak Asplund spaceValdivia compact spaceprojectional skeletonboundarycompact convex setdescriptive propertiesrenormingsuniform Kadec-Klee normLipschitz homeomorphismretractGurarij spacebinormality

Public support

  • Provider

    Academy of Sciences of the Czech Republic

  • Programme

    Grants of distinctly investigative character focused on the sphere of research pursued at present particularly in the Academy of Sciences of the Czech Republic

  • Call for proposals

    Výzkumné granty 9 (SAV02009-A)

  • Main participants

  • Contest type

    VS - Public tender

  • Contract ID

    IAA100190901

Alternative language

  • Project name in Czech

    Topologické a geometrické struktury v Banachovych prostorech

  • Annotation in Czech

    Stabilita slabých Asplundových a gateauxovsky diferencovatelných prostorů, Banachovy prostory s projekčním skeletonem, stabilita Valdiviových kompaktů, topologické charakterizace některých tříd B. prostorů, kompaktní konvexní množiny- dualita kompaktníchprostorů a B. prostorů a topologická klasifikace, slabá topologie slabých K-analytických B. prostorů, geometrické vlastnosti hranic kompaktních konvexních množin, silně afinní funkce a Baireovy třídy B. prostorů, isometrické vlastnosti L_1-preduálů, deskriptivní vlastnosti množiny derivací funkcí na B. prostoru, deskriptivní vlastnosti normových a slabých topologií na Banachových prostorech, binormalita v B. prostorech, prostory spojitých funkcí, renormace a diferencovatelnost, slabě* uniformně Kadecovy-Kleeovy normy, lipschitzovské homeomorfismy, Markuševičovy base, rozšiřování specielních lipschitzovských zobrazení, retrakty,absolutně minimální lipschitzovské funkce,Gurarijův prostor, kompakty s dodatečnou strukturou

Scientific branches

  • R&D category

    ZV - Basic research

  • CEP classification - main branch

    BA - General mathematics

  • CEP - secondary branch

  • CEP - another secondary branch

  • 10101 - Pure mathematics

Completed project evaluation

  • Provider evaluation

    V - Vynikající výsledky projektu (s mezinárodním významem atd.)

  • Project results evaluation

    Preserving completeness under very general maps;characterizations of C(X) spaces within several categories;quantitative versions of properties of Banach spaces; new results of Banach-Stone type; existence of approximate fixed points; descriptive compacts

Solution timeline

  • Realization period - beginning

    Jan 1, 2009

  • Realization period - end

    Dec 31, 2011

  • Project status

    U - Finished project

  • Latest support payment

    Mar 18, 2011

Data delivery to CEP

  • Confidentiality

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

  • Data delivery code

    CEP12-AV0-IA-U/02:2

  • Data delivery date

    Jun 28, 2013

Finance

  • Total approved costs

    2,274 thou. CZK

  • Public financial support

    2,274 thou. CZK

  • Other public sources

    0 thou. CZK

  • Non public and foreign sources

    0 thou. CZK

Basic information

Recognised costs

2 274 CZK thou.

Public support

2 274 CZK thou.

100%


Provider

Academy of Sciences of the Czech Republic

CEP

BA - General mathematics

Solution period

01. 01. 2009 - 31. 12. 2011