Matches in SemOpenAlex for { <https://semopenalex.org/work/W2029839905> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W2029839905 endingPage "469" @default.
- W2029839905 startingPage "459" @default.
- W2029839905 abstract "For a Banach space E with Schauder basis, we prove that the n fold symmetric ⊗ˆµ_n__E_ has a Schauder basis for all symmetric uniform crossnorms µ. This is done by modifying the square ordering on ℕ_n_ and showing that the new ordering gives tensor product bases in both ⊗ˆµ_n__E_ and ⊗ˆµ,s_n__E_. The main purpose of this article is to prove that the n-fold symmetric tensor product of a (real or complex) Banach space E has a Schauder basis whenever E does. The result was stated without proof in Ryan’s thesis [11] and has been constantly referred to in the literature. In the particular case of a shrinking Schauder basis for a complex Banach space E, an implicit proof was given by Dimant and Dineen [2]. The existence of a basis for the full tensor product was proved by Gelbaum and Gil de Lamadrid [7] who also showed that the unconditionality of the basis for E does not necessarily imply the same property for the tensor product basis. This was taken further by Kwapień and Pelczyński [8] who treated this issue in the context of spaces of matrices and by Pisier [9] and Schütt [12]. The dual problem, whether the monomials are a basis in the space of homogeneous polynomials, was dealt with by Dimant in her thesis [1], as well as in two other articles, together with Dineen [2] and Zalduendo [3]. The unconditionality (or lack thereof) of the monomial basis was extensively analysed by Defant, Díaz, García and Maestre [4]." @default.
- W2029839905 created "2016-06-24" @default.
- W2029839905 creator A5023933728 @default.
- W2029839905 creator A5042700028 @default.
- W2029839905 date "2005-01-01" @default.
- W2029839905 modified "2023-09-24" @default.
- W2029839905 title "Schauder bases for symmetric tensor products" @default.
- W2029839905 cites W1509568713 @default.
- W2029839905 cites W1590432342 @default.
- W2029839905 cites W176204069 @default.
- W2029839905 cites W1982157240 @default.
- W2029839905 cites W2016080679 @default.
- W2029839905 cites W2070530652 @default.
- W2029839905 cites W2081183814 @default.
- W2029839905 cites W2083549901 @default.
- W2029839905 cites W2236592434 @default.
- W2029839905 cites W2249368595 @default.
- W2029839905 cites W2571840422 @default.
- W2029839905 cites W996767716 @default.
- W2029839905 doi "https://doi.org/10.2977/prims/1145475364" @default.
- W2029839905 hasPublicationYear "2005" @default.
- W2029839905 type Work @default.
- W2029839905 sameAs 2029839905 @default.
- W2029839905 citedByCount "46" @default.
- W2029839905 countsByYear W20298399052012 @default.
- W2029839905 countsByYear W20298399052014 @default.
- W2029839905 countsByYear W20298399052015 @default.
- W2029839905 countsByYear W20298399052016 @default.
- W2029839905 countsByYear W20298399052018 @default.
- W2029839905 countsByYear W20298399052019 @default.
- W2029839905 crossrefType "journal-article" @default.
- W2029839905 hasAuthorship W2029839905A5023933728 @default.
- W2029839905 hasAuthorship W2029839905A5042700028 @default.
- W2029839905 hasBestOaLocation W20298399051 @default.
- W2029839905 hasConcept C114614502 @default.
- W2029839905 hasConcept C118615104 @default.
- W2029839905 hasConcept C124007464 @default.
- W2029839905 hasConcept C12426560 @default.
- W2029839905 hasConcept C132954091 @default.
- W2029839905 hasConcept C134306372 @default.
- W2029839905 hasConcept C20178491 @default.
- W2029839905 hasConcept C202444582 @default.
- W2029839905 hasConcept C2524010 @default.
- W2029839905 hasConcept C33923547 @default.
- W2029839905 hasConcept C51255310 @default.
- W2029839905 hasConcept C520416788 @default.
- W2029839905 hasConcept C76801838 @default.
- W2029839905 hasConcept C93776189 @default.
- W2029839905 hasConceptScore W2029839905C114614502 @default.
- W2029839905 hasConceptScore W2029839905C118615104 @default.
- W2029839905 hasConceptScore W2029839905C124007464 @default.
- W2029839905 hasConceptScore W2029839905C12426560 @default.
- W2029839905 hasConceptScore W2029839905C132954091 @default.
- W2029839905 hasConceptScore W2029839905C134306372 @default.
- W2029839905 hasConceptScore W2029839905C20178491 @default.
- W2029839905 hasConceptScore W2029839905C202444582 @default.
- W2029839905 hasConceptScore W2029839905C2524010 @default.
- W2029839905 hasConceptScore W2029839905C33923547 @default.
- W2029839905 hasConceptScore W2029839905C51255310 @default.
- W2029839905 hasConceptScore W2029839905C520416788 @default.
- W2029839905 hasConceptScore W2029839905C76801838 @default.
- W2029839905 hasConceptScore W2029839905C93776189 @default.
- W2029839905 hasIssue "2" @default.
- W2029839905 hasLocation W20298399051 @default.
- W2029839905 hasOpenAccess W2029839905 @default.
- W2029839905 hasPrimaryLocation W20298399051 @default.
- W2029839905 hasRelatedWork W2029839905 @default.
- W2029839905 hasRelatedWork W2087906067 @default.
- W2029839905 hasRelatedWork W2139736098 @default.
- W2029839905 hasRelatedWork W2186765725 @default.
- W2029839905 hasRelatedWork W2337480826 @default.
- W2029839905 hasRelatedWork W2883998132 @default.
- W2029839905 hasRelatedWork W2906753186 @default.
- W2029839905 hasRelatedWork W2963046382 @default.
- W2029839905 hasRelatedWork W4237519451 @default.
- W2029839905 hasRelatedWork W4294596685 @default.
- W2029839905 hasVolume "41" @default.
- W2029839905 isParatext "false" @default.
- W2029839905 isRetracted "false" @default.
- W2029839905 magId "2029839905" @default.
- W2029839905 workType "article" @default.