Pub Date : 1988-12-19DOI: 10.1016/S1385-7258(88)80023-4
Kazimierz Wjodarczyk
We study the problem of the existence of the angular derivative of Fréchet-holomorphic maps of the generalized right half-planes defined by non-zero partial isometries in infinite dimensional complex Banach spaces called J*-algebras. These generalized right half-planes and open unit balls (which are bounded symmetric homogeneous domains) are holomorphically equivalent. The results obtained here also hold in C *-algebras, JC*-algebras, B *-algebras and ternary algebras, containing non-zero partial isometries, and in complex Hilbert spaces. Some examples are given. The principal tool we use are general results of the Pick-Julia type in J*-algebras.
{"title":"The angular derivative of Fréchet-holomorphic maps in J*-algebras and complex Hilbert spaces","authors":"Kazimierz Wjodarczyk","doi":"10.1016/S1385-7258(88)80023-4","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80023-4","url":null,"abstract":"<div><p>We study the problem of the existence of the angular derivative of Fréchet-holomorphic maps of the generalized right half-planes defined by non-zero partial isometries in infinite dimensional complex Banach spaces called <em>J</em><sup>*</sup>-algebras. These generalized right half-planes and open unit balls (which are bounded symmetric homogeneous domains) are holomorphically equivalent. The results obtained here also hold in C <sup>*</sup>-algebras, <em>JC</em><sup>*</sup>-algebras, B <sup>*</sup>-algebras and ternary algebras, containing non-zero partial isometries, and in complex Hilbert spaces. Some examples are given. The principal tool we use are general results of the Pick-Julia type in <em>J</em><sup>*</sup>-algebras.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 455-468"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80023-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72243390","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}
Pub Date : 1988-12-19DOI: 10.1016/S1385-7258(88)80019-2
D. van Dulst
{"title":"On inner and outer convex cores of bounded sets with an application to Gδ-embeddings of 1[0,1]","authors":"D. van Dulst","doi":"10.1016/S1385-7258(88)80019-2","DOIUrl":"10.1016/S1385-7258(88)80019-2","url":null,"abstract":"","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 405-417"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80019-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"105577480","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80009-X
F.J. van der Linden
Let A be an integrally closed subring of a function field K defined over a finite field. In this paper we investigate whether the subring of K[X], consisting of those polynomials ƒ with ƒ[A]⊂A, has an A-basis {gi: i ∈ ℤZ≥0}, with deg (gi) = i.
{"title":"Integer valued polynomials over function fields","authors":"F.J. van der Linden","doi":"10.1016/S1385-7258(88)80009-X","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80009-X","url":null,"abstract":"<div><p>Let <em>A</em> be an integrally closed subring of a function field <em>K</em> defined over a finite field. In this paper we investigate whether the subring of <em>K[X]</em>, consisting of those polynomials ƒ with ƒ[<em>A</em>]⊂<em>A</em>, has an <em>A</em>-basis {g<sub>i</sub>: i ∈ ℤZ<sub>≥0</sub>}, with deg (<em>g<sub>i</sub>) = i</em>.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 293-308"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80009-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89990962","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80004-0
R.W. Cross
Let D(T)⊂X→Y be an unbounded linear operator where X and Y are normed spaces. It is shown that if Y is complete then T is strictly singular if and only if T is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which Y is not complete.
{"title":"Unbounded strictly singular operators","authors":"R.W. Cross","doi":"10.1016/S1385-7258(88)80004-0","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80004-0","url":null,"abstract":"<div><p>Let <em>D(T)⊂X→Y</em> be an unbounded linear operator where <em>X</em> and <em>Y</em> are normed spaces. It is shown that if <em>Y</em> is complete then <em>T</em> is strictly singular if and only if <em>T</em> is the sum of a continuous strictly singular operator and an unbounded finite rank operator. A counterexample is constructed for the case in which <em>Y</em> is not complete.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 245-248"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80004-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90124929","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80013-1
T.R. Sundararaman
{"title":"Characterisation of certain varieties of associative rings","authors":"T.R. Sundararaman","doi":"10.1016/S1385-7258(88)80013-1","DOIUrl":"10.1016/S1385-7258(88)80013-1","url":null,"abstract":"","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 339-341"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80013-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"112784118","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80006-4
N. de Grande-de Kimpe , C. Perez-Garcia
Several properties of non-archimedean weakly closed subspaces in connection with the extension of continuous linear functionals are studied in this paper.
研究了非阿基米德弱闭子空间与连续线性泛函的扩展有关的几个性质。
{"title":"Weakly closed subspaces and the Hahn-Banach extension property in p-adic analysis","authors":"N. de Grande-de Kimpe , C. Perez-Garcia","doi":"10.1016/S1385-7258(88)80006-4","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80006-4","url":null,"abstract":"<div><p>Several properties of non-archimedean weakly closed subspaces in connection with the extension of continuous linear functionals are studied in this paper.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 253-261"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80006-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91756099","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80005-2
Giorgio Ferrarese , Daniela Romagnoli
In this paper we prove that, if C is an elliptic curve of degree d on a general hypersurface V of degree 7 of ℙ4, then d is a multiple of 7.
证明了在广义超曲面V上，如果C是一条7次的椭圆曲线，则d是7的倍数。
{"title":"Elliptic curves on the general hypersurface of degree 7 of ℙ4","authors":"Giorgio Ferrarese , Daniela Romagnoli","doi":"10.1016/S1385-7258(88)80005-2","DOIUrl":"10.1016/S1385-7258(88)80005-2","url":null,"abstract":"<div><p>In this paper we prove that, if <em>C</em> is an elliptic curve of degree <em>d</em> on a general hypersurface <em>V</em> of degree 7 of ℙ<sup>4</sup>, then <em>d</em> is a multiple of 7.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 249-252"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80005-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"104475247","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80010-6
John T. Masterson
It is first established that there exist linear manifolds of branched affine structures having certain nonpolar branch divisors and simple polar divisors on an arbitrary compact Riemann surface M of genus g≤1. When ≥2, it is shown that these linear manifolds form a complex analytic vector bundle over the manifold of simple polar divisors on M. When g=1, elliptic functions are used to construct certain projective structures on M. A partial determination is made as to which of these projective structures are affine and which are not.
{"title":"Branched affine and projective structures on compact Riemann surfaces","authors":"John T. Masterson","doi":"10.1016/S1385-7258(88)80010-6","DOIUrl":"10.1016/S1385-7258(88)80010-6","url":null,"abstract":"<div><p>It is first established that there exist linear manifolds of branched affine structures having certain nonpolar branch divisors and simple polar divisors on an arbitrary compact Riemann surface <em>M</em> of genus <em>g≤1</em>. When <em>≥2</em>, it is shown that these linear manifolds form a complex analytic vector bundle over the manifold of simple polar divisors on <em>M</em>. When <em>g=1</em>, elliptic functions are used to construct certain projective structures on <em>M</em>. A partial determination is made as to which of these projective structures are affine and which are not.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 309-319"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80010-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109993601","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}
Pub Date : 1988-09-26DOI: 10.1016/S1385-7258(88)80007-6
N.S. Hekster, R.W. van der Waall
A fair classification of groups of prime-power order can be given, when employing the equivalence relation brought out by Ph. Hall, called n-isoclinism (n≥0). In this paper n-isoclinism is studied from a character theoretic point of view in case n=0, 1 or 2. It is known that being an M-group is invariant under 1-isoclinism and that under 2-isoclinism this does not hold in general. However, under suitable oddness assumptions on the groups in question, the invariance under 2-isoclinism of being an M-group will be established in an important special case.
{"title":"Monomiality and 2-isoclinism of groups","authors":"N.S. Hekster, R.W. van der Waall","doi":"10.1016/S1385-7258(88)80007-6","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80007-6","url":null,"abstract":"<div><p>A fair classification of groups of prime-power order can be given, when employing the equivalence relation brought out by Ph. Hall, called <em>n</em>-isoclinism (<em>n≥0</em>). In this paper <em>n</em>-isoclinism is studied from a character theoretic point of view in case <em>n=0</em>, 1 or 2. It is known that being an <em>M</em>-group is invariant under 1-isoclinism and that under 2-isoclinism this does not hold in general. However, under suitable oddness assumptions on the groups in question, the invariance under 2-isoclinism of being an <em>M</em>-group will be established in an important special case.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 263-276"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80007-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90124927","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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