{"title":"An application of Nienhuys-Thiemann's theorem to Ring derivations on H(G)","authors":"N.R. Nandakumar","doi":"10.1016/S1385-7258(88)80027-1","DOIUrl":"10.1016/S1385-7258(88)80027-1","url":null,"abstract":"<div><p>In this paper as an application of Nienhuys-Thiemann's theorem we show that a ring derivation on <em>H(G)</em>, the algebra of analytic functions on a region <em>G</em>, is linear.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 2","pages":"Pages 199-203"},"PeriodicalIF":0.0,"publicationDate":"1988-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80027-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"94414729","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":"Projective resolutions of the quotient of two ideals","authors":"Ruud Pellikaan","doi":"10.1016/1385-7258(88)90008-X","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90008-X","url":null,"abstract":"","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 65-84"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90008-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92004859","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":"An optimal lower bound for the discrepancy of c-uniformly distributed functions modulo","authors":"Michael Drmota","doi":"10.1016/1385-7258(88)90004-2","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90004-2","url":null,"abstract":"<div><p>It is proved that a lower bound for the discrepancy <em>D</em><sub><em>T</em></sub>(<em>ω</em>) of a continuous function <em>ω</em>(<em>t</em>) modulo 1 is given by <em>ϕ</em>(<em>s</em>(<em>T</em>)) infinitely often, where <em>ϕ</em>(<em>x</em>) is integrable on [0, ∞). This bound is best possible in the one dimensional case. Furthermore a generalization to compact, metric spaces is given.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 21-28"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90004-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91969055","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":"p-adic representative functions on abelian groups","authors":"G.F. Borm, W.H. Schikhof, H. de Vries","doi":"10.1016/1385-7258(88)90002-9","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90002-9","url":null,"abstract":"<div><p>The main result is the following. Let <em>G</em> be an abelian group, let <em>K</em> be an algebraically closed field of characteristic zero. Let <em>A</em> be any shift-invariant <em>K</em>-algebra with unit element of representative functions <em>G</em>→<em>K</em>, invariant under the antipode. Then the additive homomorphisms <em>G</em>→<em>K</em> in <em>A</em> together with the multiplicative homomorphisms <span><math><mtext>G→K</mtext><msup><mi></mi><mn>∗</mn></msup></math></span> in A generate A (Theorem 1.1). In § 2 a few consequences for <em>p</em>-adic representative functions are discussed.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 9-13"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90002-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91969059","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":"On the modulus of L- and M-weakly compact operators","authors":"Klaus D. Schmidt","doi":"10.1016/1385-7258(88)90010-8","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90010-8","url":null,"abstract":"<div><p>In the present paper it is shown that every <em>L</em>-weakly compact operator from an <em>AL</em>-space into a <em>KB</em>-space has an <em>L</em>-weakly compact modulus and that every <em>M</em>-weakly compact operator from a Banach lattice into an order complete <em>AM</em>-space with unit has an <em>M</em>-weakly compact modulus.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 89-92"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90010-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92122419","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 Plancherel formula for the isotropic cone","authors":"G. van Dijk","doi":"10.1016/1385-7258(88)90003-0","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90003-0","url":null,"abstract":"<div><p>In this short note we propose a definition of the isotropic cone related to a semisimple symmetric space and derive a Plancherel formula for this cone.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 15-19"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90003-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91969058","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":"On compactoidity in non-archimedean locally convex spaces with a Schauder basis","authors":"C. Pérez-Garcia","doi":"10.1016/1385-7258(88)90009-1","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90009-1","url":null,"abstract":"<div><p>Several properties of compactoid sets in non-archimedean locally convex spaces with a Schauder basis are proved in this paper. As a consequence we derive partial affirmative answers to the questions formulated by Gruson and Van der Put ([4], problem following 5.8) and Schikhof ([6], problem following 1.7), respectively.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 85-88"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90009-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91969062","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":"On Lipschitz-type maximal functions and their smoothness spaces","authors":"Burkhard Lenze","doi":"10.1016/1385-7258(88)90007-8","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90007-8","url":null,"abstract":"<div><p>In a recent monograph (cf. No. 293 of the Memoirs of the Amer. Math. Soc. 47 (1984)) DeVore and Sharpley study maximal functions of integral type and their related smoothness spaces. One of their central results gives an embedding theorem for the smoothness spaces in terms of Besov spaces. In this paper we consider the related problem when the Besov spaces are substituted by the so-called A-spaces introduced by Popov (take the τ-modulus instead of the ω-modulus). We will define Lipschitz-type maximal functions whose smoothness spaces satisfy a corresponding embedding theorem in terms of <em>A</em>-spaces. By well-known results new insights can only be expected for functions satisfying low order smoothness conditions and, therefore, only function spaces generated by first order differences are considered.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 53-63"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90007-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91969057","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":"Elements with unit spectrum in a Banach lattice algebra","authors":"C.B. Huijsmans","doi":"10.1016/1385-7258(88)90006-6","DOIUrl":"https://doi.org/10.1016/1385-7258(88)90006-6","url":null,"abstract":"<div><p>It is the aim of the present paper to give an elementary proof of the following theorem.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 1","pages":"Pages 43-51"},"PeriodicalIF":0.0,"publicationDate":"1988-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(88)90006-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92118167","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}