{"title":"Order structure of the semigroup dual: a counterexample","authors":"A. Grabosch, R. Nagel","doi":"10.1016/S1385-7258(89)80027-7","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80027-7","url":null,"abstract":"<div><p>We give an example of a positive semigroup on a Banach lattice whose semigroup dual is not a Banach lattice.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 199-201"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80027-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92172894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The constructive theory of preference relations on a locally compact space","authors":"Douglas S. Bridges","doi":"10.1016/S1385-7258(89)80023-X","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80023-X","url":null,"abstract":"<div><p>This paper, which is written within a rigorously constructive framework, deals with preference relations (strict weak orders) on a locally compact space <em>X</em>, and with the representation of such relations by continuous utility functions (order isomorphisms) from X into ℝ. Necessary conditions are given for finding the values of a utility function algorithmically in terms of the parameters when <em>X</em> is a locally compact, convex subset of R<sup>N</sup>. These conditions single out the class of <em>admissible preference relations</em>, which are investigated in some detail. The paper concludes with some results on the algorithmic continuity of the process which assigns utility functions to admissible preference relations.</p><p>The work of this paper can be regarded as a recursive development of preference and utility theory.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 141-165"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80023-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92172897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Full and fundamental partial orderings","authors":"Ph. Dwinger","doi":"10.1016/S1385-7258(89)80024-1","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80024-1","url":null,"abstract":"<div><p>The number of full, and the number of fundamental partial orderings on a finite set are determined. Also, the structure of the partially ordered set of full suborderings of a finite chain is investigated.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 167-173"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80024-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92219648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Eigenvalues of absolute Cesàro matrices","authors":"I.J. Maddox","doi":"10.1016/S1385-7258(89)80029-0","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80029-0","url":null,"abstract":"<div><p>A complete description is given of the eigenvalues of the matrix <em>A</em> associated with absolute Cesàro summability of any positive order, where <em>A</em> is regarded as an operator on the Banach space <em>l<sub>p</sub></em>, with 1 ≤<em>p</em>≤ ∞.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 213-217"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80029-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92172895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Gevrey space characterization of certain Gelfand-Shilov spaces Sαβ","authors":"A.F.M. ter Elst, S.J.L. van Eijndhoven","doi":"10.1016/S1385-7258(89)80025-3","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80025-3","url":null,"abstract":"<div><p>Let <em>p,q</em> ∈ ℕ and let ϱ≥ϱ<sub><em>p,q</em></sub> with ϱ<sub><em>p,q</em></sub> = max {l/<em>p</em>, l/<em>q</em>}, ϱ<sub><em>p</em>1,</sub> = 1/<em>p</em>, and ϱ<sub>1,<em>q</em></sub>= 1/<em>q</em>, <em>p,q</em>>l. In this paper it is proved that there exist symmetric differential operators <em>A</em><sub><em>p,q</em></sub> in L<sub>2</sub>(ℝ) such that the Gelfand-Shilov space <em><strong>S</strong></em><sub><em>pϱ</em></sub><sup><em>pϱ</em></sup> is equal to the Gevrey space of order 2<em>pqϱ</em> relative to <em>A<sub>p,q</sub></em>.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 175-184"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80025-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92172898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A structure theorem for abstract Witt rings containing rigid elements","authors":"Rik Bos","doi":"10.1016/S1385-7258(89)80022-8","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80022-8","url":null,"abstract":"<div><p>Suppose (<em>R, G</em>) is a non-reduced abstract Witt ring containing a rigid element <em>d</em> such that the value set D<1,-<em>d</em>> satisfies a certain finiteness-condition. Then (<em>R, G</em>) is a direct product of a reduced abstract Witt ring and a Witt-group ring.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 125-140"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80022-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92172896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The bidual of a non-archimedean locally convex space","authors":"N. de Grande-de Kimpe","doi":"10.1016/S1385-7258(89)80028-9","DOIUrl":"https://doi.org/10.1016/S1385-7258(89)80028-9","url":null,"abstract":"<div><p>Semi-reflexivity and reflexivity of locally convex spaces over a field <em>K</em> with <em>a</em>, non-trivial, non-archimedean valuation are studied.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 2","pages":"Pages 203-212"},"PeriodicalIF":0.0,"publicationDate":"1989-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80028-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92219649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The continuous linear image of a p-adic compactoid","authors":"W.H. Schikhof","doi":"10.1016/S1385-7258(89)80021-6","DOIUrl":"10.1016/S1385-7258(89)80021-6","url":null,"abstract":"<div><p>The key result is the following. Let <em>A</em> be a closed (local) compactoid in a Banach space <em>E</em> over a non-archimedean valued field <em>K</em>. If <em>F</em> is a <em>K</em>-Banach space and <em>T:E→F</em> is a continuous linear map then <span><math><mrow><mover><mrow><mi>T</mi><mi>A</mi></mrow><mo>¯</mo></mover><mo>⊂</mo><mi>λ</mi><mi>T</mi><mi>A</mi></mrow></math></span> for each λ∈<em>K</em>, |λ|>1. As an application the existence of the finest admissible topology of countable type on a locally convex space is proved.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 1","pages":"Pages 119-123"},"PeriodicalIF":0.0,"publicationDate":"1989-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(89)80021-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"96583586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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