The heart of the Banach spaces

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dc.contributor.authorWegner, Sven-Ake
dc.creatorSven-Ake, Wegner
dc.date.accessioned2017-12-15T04:58:24Z
dc.date.available2017-12-15T04:58:24Z
dc.date.issued2017-11-01
dc.description.abstractAbstract Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beĭlinson, Bernstein and Deligne consider in this setting a t-structure on the derived category and remark that its heart can be described as a category of formal quotients. They further point out that the category of Banach spaces is an example, and that here a similar category of formal quotients was studied by Waelbroeck already in 1962. In the current article, we give a direct and rigorous construction of the latter category by considering first the monomorphism category. Then we localize with respect to a multiplicative system. Our approach gives rise to a heart-like category not only for the Banach spaces. In particular, the main results apply to categories in which the set of all kernel–cokernel pairs does not form an exact structure. Such categories arise frequently in functional analysis.en_US
dc.identifierDOI:10.1016/j.jpaa.2017.02.006
dc.identifier.citationSven-Ake Wegner, The heart of the Banach spaces, In Journal of Pure and Applied Algebra, Volume 221, Issue 11, 2017, Pages 2880-2909en_US
dc.identifier.issn00224049
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S0022404917300312
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/2929
dc.language.isoenen_US
dc.publisherJournal of Pure and Applied Algebraen_US
dc.relation.ispartofJournal of Pure and Applied Algebra
dc.rights.license© 2017 Elsevier B.V. All rights reserved.
dc.titleThe heart of the Banach spacesen_US
dc.typeArticleen_US
elsevier.aggregationtypeJournal
elsevier.coverdate2017-11-01
elsevier.coverdisplaydateNovember 2017
elsevier.endingpage2909
elsevier.identifier.doi10.1016/j.jpaa.2017.02.006
elsevier.identifier.eid1-s2.0-S0022404917300312
elsevier.identifier.piiS0022-4049(17)30031-2
elsevier.identifier.scopusid85014060557
elsevier.issue.identifier11
elsevier.openaccess0
elsevier.openaccessarticlefalse
elsevier.openarchivearticlefalse
elsevier.startingpage2880
elsevier.teaserConsider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beĭlinson, Bernstein...
elsevier.volume221
workflow.import.sourcescience

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