Matches in SemOpenAlex for { <https://semopenalex.org/work/W2953133693> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W2953133693 abstract "It is well known in Banach space theory that for a finite dimensional space $E$ there exists a constant $c_E$, such that for all sequences $(x_k)_k subset E$ one has [ summ_k noo x_k rrm kl c_E pl sup_{eps_k pm 1} noo summ_k eps_k x_k rrm pl .] Moreover, if $E$ is of dimension $n$ the constant $c_E$ ranges between $sqrt{n}$ and $n$. This implies that absolute convergence and unconditional convergence only coincide in finite dimensional spaces. We will characterize Banach spaces $X$, where the constant $c_E sim sqrt{n}$ for all finite dimensional subspaces. More generally, we prove that an estimate $c_E kll c n^{1-frac{1}{q}}$holds for all $n in nz$ and all $n$-dimensional subspaces $E$ of $X$ if and only if the eigenvalues of every operator factoring through $ell_{infty}$ decrease of order $k^{-frac{1}{q}}$ if and only if $X$ is of weak cotype $q$, introduced by Pisier and Mascioni. We emphasize that in contrast to Talagrand's equivalence theorem on cotype $q$ and absolutely $(q,1)$-summing spaces this extendsto the case $q=2$. If $q>2$ and one of the conditions above is satisfied one has [ kla summ_k noo x_k rrm^q mer^{frac{1}{q}} kl C^{1+l}pl (1+{rm log}_2)^{(l)}((1 +{rm log}_2 n)^{frac{1}{q}}) pl ez noo summ_k eps_k x_k rrm ] for all $n,l in nz$ and $(x_k)_k subset E$, $E$ a $n$ dimensional subspace of $X$. In the case $q=2$ the same holds if we replace the expected value by the supremum." @default.
- W2953133693 created "2019-06-27" @default.
- W2953133693 creator A5030843204 @default.
- W2953133693 date "1993-12-22" @default.
- W2953133693 modified "2023-09-27" @default.
- W2953133693 title "Cotype and summing properties in Banach spaces" @default.
- W2953133693 cites W1522013486 @default.
- W2953133693 cites W1604321310 @default.
- W2953133693 cites W2048295436 @default.
- W2953133693 hasPublicationYear "1993" @default.
- W2953133693 type Work @default.
- W2953133693 sameAs 2953133693 @default.
- W2953133693 citedByCount "0" @default.
- W2953133693 crossrefType "posted-content" @default.
- W2953133693 hasAuthorship W2953133693A5030843204 @default.
- W2953133693 hasConcept C114614502 @default.
- W2953133693 hasConcept C118615104 @default.
- W2953133693 hasConcept C12362212 @default.
- W2953133693 hasConcept C132954091 @default.
- W2953133693 hasConcept C138885662 @default.
- W2953133693 hasConcept C199360897 @default.
- W2953133693 hasConcept C2524010 @default.
- W2953133693 hasConcept C2777027219 @default.
- W2953133693 hasConcept C2778572836 @default.
- W2953133693 hasConcept C33676613 @default.
- W2953133693 hasConcept C33923547 @default.
- W2953133693 hasConcept C41008148 @default.
- W2953133693 hasConcept C41895202 @default.
- W2953133693 hasConceptScore W2953133693C114614502 @default.
- W2953133693 hasConceptScore W2953133693C118615104 @default.
- W2953133693 hasConceptScore W2953133693C12362212 @default.
- W2953133693 hasConceptScore W2953133693C132954091 @default.
- W2953133693 hasConceptScore W2953133693C138885662 @default.
- W2953133693 hasConceptScore W2953133693C199360897 @default.
- W2953133693 hasConceptScore W2953133693C2524010 @default.
- W2953133693 hasConceptScore W2953133693C2777027219 @default.
- W2953133693 hasConceptScore W2953133693C2778572836 @default.
- W2953133693 hasConceptScore W2953133693C33676613 @default.
- W2953133693 hasConceptScore W2953133693C33923547 @default.
- W2953133693 hasConceptScore W2953133693C41008148 @default.
- W2953133693 hasConceptScore W2953133693C41895202 @default.
- W2953133693 hasLocation W29531336931 @default.
- W2953133693 hasOpenAccess W2953133693 @default.
- W2953133693 hasPrimaryLocation W29531336931 @default.
- W2953133693 hasRelatedWork W101515012 @default.
- W2953133693 hasRelatedWork W101911525 @default.
- W2953133693 hasRelatedWork W123832256 @default.
- W2953133693 hasRelatedWork W1603828255 @default.
- W2953133693 hasRelatedWork W1890055089 @default.
- W2953133693 hasRelatedWork W1965052742 @default.
- W2953133693 hasRelatedWork W1988272554 @default.
- W2953133693 hasRelatedWork W2015290844 @default.
- W2953133693 hasRelatedWork W2020339284 @default.
- W2953133693 hasRelatedWork W2047580653 @default.
- W2953133693 hasRelatedWork W2552788888 @default.
- W2953133693 hasRelatedWork W2589555890 @default.
- W2953133693 hasRelatedWork W2625068759 @default.
- W2953133693 hasRelatedWork W2734660468 @default.
- W2953133693 hasRelatedWork W2890050480 @default.
- W2953133693 hasRelatedWork W2950446373 @default.
- W2953133693 hasRelatedWork W2952025868 @default.
- W2953133693 hasRelatedWork W2962911525 @default.
- W2953133693 hasRelatedWork W2963970509 @default.
- W2953133693 hasRelatedWork W2964132519 @default.
- W2953133693 isParatext "false" @default.
- W2953133693 isRetracted "false" @default.
- W2953133693 magId "2953133693" @default.
- W2953133693 workType "article" @default.