Matches in SemOpenAlex for { <https://semopenalex.org/work/W2904011694> ?p ?o ?g. }
Showing items 1 to 76 of
76
with 100 items per page.
- W2904011694 endingPage "586" @default.
- W2904011694 startingPage "574" @default.
- W2904011694 abstract "For a constant $Kgeq 1$, let $mathfrak{B}_K$ be the class of pairs $(X,(mathbf e_n)_{ninomega})$ consisting of a Banach space $X$ and an unconditional Schauder basis $(mathbf e_n)_{ninomega}$ for $X$, having the unconditional basic constant $K_ule K$. Such pairs are called $K$-based Banach spaces. A based Banach space $X$ is rational if the unit ball of any finite-dimensional subspace spanned by finitely many basic vectors is a polyhedron whose vertices have rational coordinates in the Schauder basis of $X$. Using the technique of Fraïssé theory, we construct a rational $K$-based Banach space $big(mathbb U_K,(mathbf e_n)_{ninomega}big)$ which is $mathfrak{RI}_K$-universal in the sense that each basis preserving isometry $f:Lambdatomathbb U_K$ defined on a based subspace $Lambda$ of a finite-dimensional rational $K$-based Banach space $A$ extends to a basis preserving isometry $bar f:Atomathbb U_K$ of the based Banach space $A$. We also prove that the $K$-based Banach space $mathbb U_K$ is almost $mathfrak{FI}_1$-universal in the sense that any base preserving $varepsilon$-isometry $f:Lambdatomathbb U_K$ defined on a based subspace $Lambda$ of a finite-dimensional $1$-based Banach space $A$ extends to a base preserving $varepsilon$-isometry $bar f:Atomathbb U_K$ of the based Banach space $A$. On the other hand, we show that no almost $mathfrak{FI}_K$-universal based Banach space exists for $K>1$. The Banach space $mathbb U_K$ is isomorphic to the complementably universal Banach space for the class of Banach spaces with an unconditional Schauder basis, constructed by Pełczyński in 1969." @default.
- W2904011694 created "2018-12-22" @default.
- W2904011694 creator A5053575143 @default.
- W2904011694 creator A5088614199 @default.
- W2904011694 date "2019-04-01" @default.
- W2904011694 modified "2023-10-18" @default.
- W2904011694 title "A universal Banach space with a $K$-unconditional basis" @default.
- W2904011694 doi "https://doi.org/10.15352/aot.1805-1369" @default.
- W2904011694 hasPublicationYear "2019" @default.
- W2904011694 type Work @default.
- W2904011694 sameAs 2904011694 @default.
- W2904011694 citedByCount "2" @default.
- W2904011694 countsByYear W29040116942018 @default.
- W2904011694 countsByYear W29040116942020 @default.
- W2904011694 crossrefType "journal-article" @default.
- W2904011694 hasAuthorship W2904011694A5053575143 @default.
- W2904011694 hasAuthorship W2904011694A5088614199 @default.
- W2904011694 hasBestOaLocation W29040116942 @default.
- W2904011694 hasConcept C114614502 @default.
- W2904011694 hasConcept C118615104 @default.
- W2904011694 hasConcept C120665830 @default.
- W2904011694 hasConcept C121332964 @default.
- W2904011694 hasConcept C12426560 @default.
- W2904011694 hasConcept C132954091 @default.
- W2904011694 hasConcept C134306372 @default.
- W2904011694 hasConcept C191948623 @default.
- W2904011694 hasConcept C202444582 @default.
- W2904011694 hasConcept C2524010 @default.
- W2904011694 hasConcept C2778113609 @default.
- W2904011694 hasConcept C2779557605 @default.
- W2904011694 hasConcept C32834561 @default.
- W2904011694 hasConcept C33923547 @default.
- W2904011694 hasConcept C42058472 @default.
- W2904011694 hasConcept C62520636 @default.
- W2904011694 hasConcept C76801838 @default.
- W2904011694 hasConcept C82457910 @default.
- W2904011694 hasConceptScore W2904011694C114614502 @default.
- W2904011694 hasConceptScore W2904011694C118615104 @default.
- W2904011694 hasConceptScore W2904011694C120665830 @default.
- W2904011694 hasConceptScore W2904011694C121332964 @default.
- W2904011694 hasConceptScore W2904011694C12426560 @default.
- W2904011694 hasConceptScore W2904011694C132954091 @default.
- W2904011694 hasConceptScore W2904011694C134306372 @default.
- W2904011694 hasConceptScore W2904011694C191948623 @default.
- W2904011694 hasConceptScore W2904011694C202444582 @default.
- W2904011694 hasConceptScore W2904011694C2524010 @default.
- W2904011694 hasConceptScore W2904011694C2778113609 @default.
- W2904011694 hasConceptScore W2904011694C2779557605 @default.
- W2904011694 hasConceptScore W2904011694C32834561 @default.
- W2904011694 hasConceptScore W2904011694C33923547 @default.
- W2904011694 hasConceptScore W2904011694C42058472 @default.
- W2904011694 hasConceptScore W2904011694C62520636 @default.
- W2904011694 hasConceptScore W2904011694C76801838 @default.
- W2904011694 hasConceptScore W2904011694C82457910 @default.
- W2904011694 hasIssue "3" @default.
- W2904011694 hasLocation W29040116941 @default.
- W2904011694 hasLocation W29040116942 @default.
- W2904011694 hasOpenAccess W2904011694 @default.
- W2904011694 hasPrimaryLocation W29040116941 @default.
- W2904011694 hasRelatedWork W1485674099 @default.
- W2904011694 hasRelatedWork W1624826081 @default.
- W2904011694 hasRelatedWork W1638130911 @default.
- W2904011694 hasRelatedWork W2009653049 @default.
- W2904011694 hasRelatedWork W2070488704 @default.
- W2904011694 hasRelatedWork W2468734465 @default.
- W2904011694 hasRelatedWork W2952325882 @default.
- W2904011694 hasRelatedWork W4293496984 @default.
- W2904011694 hasRelatedWork W4300715189 @default.
- W2904011694 hasRelatedWork W950405407 @default.
- W2904011694 hasVolume "4" @default.
- W2904011694 isParatext "false" @default.
- W2904011694 isRetracted "false" @default.
- W2904011694 magId "2904011694" @default.
- W2904011694 workType "article" @default.