naa a22 4500 510782760 CHVBK 20180411083252.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s11856-012-0115-z doi (NATIONALLICENCE)springer-10.1007/s11856-012-0115-z On the Borelness of the intersection operation [Elektronische Daten] [Longyun Ding, Su Gao] We study the intersection operation of closed linear subspaces in a separable Banach space. We show that if the ambient space is quasi-reflexive, then the intersection operation is Borel. On the other hand, if the space contains a closed subspace with a Schauder decomposition into infinitely many non-reflexive spaces, then the intersection operation is not Borel. As a corollary, for a closed subspace of a Banach space with an unconditional basis, the intersection operation of the closed linear subspaces is Borel if and only if the space is reflexive. We also consider the intersection operation of additive subgroups in an infinite-dimensional separable Banach space, and show that if this intersection operation is Borel then the space is hereditarily indecomposable. Hebrew University Magnes Press, 2013 Ding Longyun School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, China aut Gao Su Department of Mathematics, University of North Texas, 1155 Union Circle #311430, 76203-5017, Denton, TX, USA aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 783-800 0021-2172 195:2<783 2013 195 11856 https://doi.org/10.1007/s11856-012-0115-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0115-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Ding Longyun School of Mathematical Sciences and LPMC, Nankai University, 300071, Tianjin, China aut NATIONALLICENCE 700 1- Gao Su Department of Mathematics, University of North Texas, 1155 Union Circle #311430, 76203-5017, Denton, TX, USA aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 195/2(2013-06-01), 783-800 0021-2172 195:2<783 2013 195 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer