Steinhaus' lattice-point problem for Banach spaces

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dc.contributor.author Kania, Tomasz
dc.contributor.author Kochanek, Tomasz
dc.date.accessioned 2017-11-15T12:01:22Z
dc.date.available 2017-11-15T12:01:22Z
dc.date.issued 2017-02-15
dc.identifier.citation Kania, T. and Kochanek, T. (2017) ‘Steinhaus' lattice-point problem for Banach spaces’, Journal of Mathematical Analysis and Applications, 446(2), pp. 1219-1229. doi:10.1016/j.jmaa.2016.09.030 en
dc.identifier.volume 446 en
dc.identifier.issued 2 en
dc.identifier.startpage 1219 en
dc.identifier.endpage 1229 en
dc.identifier.issn 0022-247X
dc.identifier.uri http://hdl.handle.net/10468/5053
dc.identifier.doi 10.1016/j.jmaa.2016.09.030
dc.description.abstract Steinhaus proved that given a positive integer n, one may find a circle surrounding exactly n points of the integer lattice. This statement has been recently extended to Hilbert spaces by Zwoleński, who replaced the integer lattice by any infinite set that intersects every ball in at most finitely many points. We investigate Banach spaces satisfying this property, which we call (S), and characterise them by means of a new geometric property of the unit sphere which allows us to show, e.g., that all strictly convex norms have (S), nonetheless, there are plenty of non-strictly convex norms satisfying (S). We also study the corresponding renorming problem. en
dc.description.sponsorship Ministerstwo Nauki i Szkolnictwa Wyższego (Project No. IP2012011072) en
dc.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher Elsevier Ltd. en
dc.rights © 2017, Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license. en
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ en
dc.subject Steinhaus' problem en
dc.subject Lattice points en
dc.subject Strictly convex space en
dc.title Steinhaus' lattice-point problem for Banach spaces en
dc.type Article (peer-reviewed) en
dc.internal.authorcontactother Tomasz Kania, Mathematical Sciences, University College Cork, Cork, Ireland. T: +353-21-490-3000 E: tomasz.marcin.kania@gmail.com en
dc.internal.availability Full text available en
dc.check.info Access to this article is restricted until 24 months after publication by request of the publisher. en
dc.check.date 2019-02-15
dc.description.version Accepted Version en
dc.contributor.funder European Research Council en
dc.contributor.funder Ministerstwo Nauki i Szkolnictwa Wyższego en
dc.description.status Peer reviewed en
dc.identifier.journaltitle Journal of Mathematical Analysis and Applications en
dc.internal.IRISemailaddress tomasz.marcin.kania@gmail.com en
dc.relation.project info:eu-repo/grantAgreement/EC/FP7::SP2::ERC/291497/EU/Local Structure of Sets, Measures and Currents/LOCALSTRUCTURE en


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© 2017, Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license. Except where otherwise noted, this item's license is described as © 2017, Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.
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