Matches in SemOpenAlex for { <https://semopenalex.org/work/W2951782344> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2951782344 abstract "We first prove that in a sigma-finite von Neumann factor M, a positive element $a$ with properly infinite range projection R_a is a linear combination of projections with positive coefficients if and only if the essential norm ||a||_e with respect to the closed two-sided ideal J(M) generated by the finite projections of M does not vanish. Then we show that if ||a||_e>1, then a is a finite sum of projections. Both these results are extended to general properly infinite von Neumann algebras in terms of central essential spectra. Secondly, we provide a necessary condition for a positive operator a to be a finite sum of projections in terms of the principal ideals generated by the excess part a_+:=(a-I)chi_a(1,infty) and the defect part a_-:= (I-a)chi_a(0, 1) of a; this result appears to be new also for B(H). Thirdly, we prove that in a type II_1 factor a sufficient condition for a positive diagonalizable operators to be a finite sum of projections is that tau(a_+)- tau(a_-)>0." @default.
- W2951782344 created "2019-06-27" @default.
- W2951782344 creator A5002744113 @default.
- W2951782344 creator A5003457056 @default.
- W2951782344 creator A5021243093 @default.
- W2951782344 creator A5027882881 @default.
- W2951782344 date "2010-07-27" @default.
- W2951782344 modified "2023-09-26" @default.
- W2951782344 title "Finite sums of projections in von Neumann algebras" @default.
- W2951782344 cites W1524878283 @default.
- W2951782344 cites W1529328961 @default.
- W2951782344 cites W1533213248 @default.
- W2951782344 cites W1635573508 @default.
- W2951782344 cites W1663412835 @default.
- W2951782344 cites W1893249576 @default.
- W2951782344 cites W1973862789 @default.
- W2951782344 cites W1984474434 @default.
- W2951782344 cites W1996869014 @default.
- W2951782344 cites W2004058694 @default.
- W2951782344 cites W2009029203 @default.
- W2951782344 cites W2034158226 @default.
- W2951782344 cites W2042379111 @default.
- W2951782344 cites W2050399503 @default.
- W2951782344 cites W2058110752 @default.
- W2951782344 cites W2061232715 @default.
- W2951782344 cites W2070353086 @default.
- W2951782344 cites W2070725840 @default.
- W2951782344 cites W2071345924 @default.
- W2951782344 cites W2963927714 @default.
- W2951782344 cites W657849156 @default.
- W2951782344 doi "https://doi.org/10.48550/arxiv.1007.4679" @default.
- W2951782344 hasPublicationYear "2010" @default.
- W2951782344 type Work @default.
- W2951782344 sameAs 2951782344 @default.
- W2951782344 citedByCount "3" @default.
- W2951782344 countsByYear W29517823442012 @default.
- W2951782344 crossrefType "posted-content" @default.
- W2951782344 hasAuthorship W2951782344A5002744113 @default.
- W2951782344 hasAuthorship W2951782344A5003457056 @default.
- W2951782344 hasAuthorship W2951782344A5021243093 @default.
- W2951782344 hasAuthorship W2951782344A5027882881 @default.
- W2951782344 hasBestOaLocation W29517823441 @default.
- W2951782344 hasConcept C111472728 @default.
- W2951782344 hasConcept C11413529 @default.
- W2951782344 hasConcept C121332964 @default.
- W2951782344 hasConcept C132954091 @default.
- W2951782344 hasConcept C138885662 @default.
- W2951782344 hasConcept C153408630 @default.
- W2951782344 hasConcept C158693339 @default.
- W2951782344 hasConcept C17744445 @default.
- W2951782344 hasConcept C191795146 @default.
- W2951782344 hasConcept C199539241 @default.
- W2951782344 hasConcept C202444582 @default.
- W2951782344 hasConcept C21261745 @default.
- W2951782344 hasConcept C2776639384 @default.
- W2951782344 hasConcept C30072841 @default.
- W2951782344 hasConcept C33923547 @default.
- W2951782344 hasConcept C54848796 @default.
- W2951782344 hasConcept C57493831 @default.
- W2951782344 hasConcept C62520636 @default.
- W2951782344 hasConcept C80469333 @default.
- W2951782344 hasConcept C99392333 @default.
- W2951782344 hasConceptScore W2951782344C111472728 @default.
- W2951782344 hasConceptScore W2951782344C11413529 @default.
- W2951782344 hasConceptScore W2951782344C121332964 @default.
- W2951782344 hasConceptScore W2951782344C132954091 @default.
- W2951782344 hasConceptScore W2951782344C138885662 @default.
- W2951782344 hasConceptScore W2951782344C153408630 @default.
- W2951782344 hasConceptScore W2951782344C158693339 @default.
- W2951782344 hasConceptScore W2951782344C17744445 @default.
- W2951782344 hasConceptScore W2951782344C191795146 @default.
- W2951782344 hasConceptScore W2951782344C199539241 @default.
- W2951782344 hasConceptScore W2951782344C202444582 @default.
- W2951782344 hasConceptScore W2951782344C21261745 @default.
- W2951782344 hasConceptScore W2951782344C2776639384 @default.
- W2951782344 hasConceptScore W2951782344C30072841 @default.
- W2951782344 hasConceptScore W2951782344C33923547 @default.
- W2951782344 hasConceptScore W2951782344C54848796 @default.
- W2951782344 hasConceptScore W2951782344C57493831 @default.
- W2951782344 hasConceptScore W2951782344C62520636 @default.
- W2951782344 hasConceptScore W2951782344C80469333 @default.
- W2951782344 hasConceptScore W2951782344C99392333 @default.
- W2951782344 hasLocation W29517823441 @default.
- W2951782344 hasLocation W29517823442 @default.
- W2951782344 hasOpenAccess W2951782344 @default.
- W2951782344 hasPrimaryLocation W29517823441 @default.
- W2951782344 hasRelatedWork W1970362971 @default.
- W2951782344 hasRelatedWork W1979990741 @default.
- W2951782344 hasRelatedWork W1983366713 @default.
- W2951782344 hasRelatedWork W2068470421 @default.
- W2951782344 hasRelatedWork W2109288771 @default.
- W2951782344 hasRelatedWork W2803850028 @default.
- W2951782344 hasRelatedWork W2963457624 @default.
- W2951782344 hasRelatedWork W3017976112 @default.
- W2951782344 hasRelatedWork W3210451834 @default.
- W2951782344 hasRelatedWork W4318621076 @default.
- W2951782344 isParatext "false" @default.
- W2951782344 isRetracted "false" @default.
- W2951782344 magId "2951782344" @default.
- W2951782344 workType "article" @default.