Matches in SemOpenAlex for { <https://semopenalex.org/work/W1855852214> ?p ?o ?g. }
Showing items 1 to 77 of
77
with 100 items per page.
- W1855852214 abstract "The first part of the paper is inspired by a theorem of H. Rosenthal, that if an operator on $L_1[0,1]$ satisfies the assumption that for each measurable set $A subseteq [0,1]$ the restriction $T bigl|_{L_1(A)}$ is not an isomorphic embedding, then the operator is narrow. (Here $L_1(A) = bigl{x in L_1: ,, {rm supp} , x subseteq A bigr}$.) This leads to a natural question of finding mildest possible assumptions for operators on a given space $X$, which will imply that the operator is narrow. We find a partial answer to this question for operators on $L_p(0,1)$ with $1<p<2$. Namely we define a notion of a gentle growth of a function and we prove that for $1 < p < 2$ every operator $T$ on $L_p$ which is unbounded from below on $L_p(A)$, $A subseteq [0,1]$, by means of function having a gentle growth, is narrow. In the second part of the paper we consider the question for what Banach spaces $X$, every operator $T:L_p lra X$ is narrow. We prove that for $2 < p, r < infty$ every operator $T: L_prightarrowell_r$ is narrow, which completes the list of results for operators from $L_p$ to sequence and function Lebesgue spaces." @default.
- W1855852214 created "2016-06-24" @default.
- W1855852214 creator A5021827340 @default.
- W1855852214 creator A5024100759 @default.
- W1855852214 creator A5055084606 @default.
- W1855852214 date "2012-01-19" @default.
- W1855852214 modified "2023-09-25" @default.
- W1855852214 title "On Enflo and narrow operators acting on $L_p$" @default.
- W1855852214 cites W1509154951 @default.
- W1855852214 cites W2010304098 @default.
- W1855852214 cites W2014066661 @default.
- W1855852214 cites W2053272602 @default.
- W1855852214 cites W2085460461 @default.
- W1855852214 cites W2102883685 @default.
- W1855852214 cites W2121879857 @default.
- W1855852214 cites W2883833809 @default.
- W1855852214 doi "https://doi.org/10.48550/arxiv.1201.4041" @default.
- W1855852214 hasPublicationYear "2012" @default.
- W1855852214 type Work @default.
- W1855852214 sameAs 1855852214 @default.
- W1855852214 citedByCount "0" @default.
- W1855852214 crossrefType "posted-content" @default.
- W1855852214 hasAuthorship W1855852214A5021827340 @default.
- W1855852214 hasAuthorship W1855852214A5024100759 @default.
- W1855852214 hasAuthorship W1855852214A5055084606 @default.
- W1855852214 hasBestOaLocation W18558522141 @default.
- W1855852214 hasConcept C104317684 @default.
- W1855852214 hasConcept C114614502 @default.
- W1855852214 hasConcept C118615104 @default.
- W1855852214 hasConcept C132954091 @default.
- W1855852214 hasConcept C14036430 @default.
- W1855852214 hasConcept C154945302 @default.
- W1855852214 hasConcept C158448853 @default.
- W1855852214 hasConcept C17020691 @default.
- W1855852214 hasConcept C185592680 @default.
- W1855852214 hasConcept C202444582 @default.
- W1855852214 hasConcept C33923547 @default.
- W1855852214 hasConcept C41008148 @default.
- W1855852214 hasConcept C41608201 @default.
- W1855852214 hasConcept C55493867 @default.
- W1855852214 hasConcept C78458016 @default.
- W1855852214 hasConcept C86339819 @default.
- W1855852214 hasConcept C86803240 @default.
- W1855852214 hasConceptScore W1855852214C104317684 @default.
- W1855852214 hasConceptScore W1855852214C114614502 @default.
- W1855852214 hasConceptScore W1855852214C118615104 @default.
- W1855852214 hasConceptScore W1855852214C132954091 @default.
- W1855852214 hasConceptScore W1855852214C14036430 @default.
- W1855852214 hasConceptScore W1855852214C154945302 @default.
- W1855852214 hasConceptScore W1855852214C158448853 @default.
- W1855852214 hasConceptScore W1855852214C17020691 @default.
- W1855852214 hasConceptScore W1855852214C185592680 @default.
- W1855852214 hasConceptScore W1855852214C202444582 @default.
- W1855852214 hasConceptScore W1855852214C33923547 @default.
- W1855852214 hasConceptScore W1855852214C41008148 @default.
- W1855852214 hasConceptScore W1855852214C41608201 @default.
- W1855852214 hasConceptScore W1855852214C55493867 @default.
- W1855852214 hasConceptScore W1855852214C78458016 @default.
- W1855852214 hasConceptScore W1855852214C86339819 @default.
- W1855852214 hasConceptScore W1855852214C86803240 @default.
- W1855852214 hasLocation W18558522141 @default.
- W1855852214 hasOpenAccess W1855852214 @default.
- W1855852214 hasPrimaryLocation W18558522141 @default.
- W1855852214 hasRelatedWork W1637102167 @default.
- W1855852214 hasRelatedWork W1978042415 @default.
- W1855852214 hasRelatedWork W2031659000 @default.
- W1855852214 hasRelatedWork W2170662346 @default.
- W1855852214 hasRelatedWork W2234982114 @default.
- W1855852214 hasRelatedWork W2278466645 @default.
- W1855852214 hasRelatedWork W2766222296 @default.
- W1855852214 hasRelatedWork W3011491025 @default.
- W1855852214 hasRelatedWork W3086542228 @default.
- W1855852214 hasRelatedWork W2169668784 @default.
- W1855852214 isParatext "false" @default.
- W1855852214 isRetracted "false" @default.
- W1855852214 magId "1855852214" @default.
- W1855852214 workType "article" @default.