Acta Mathematica Hungarica最新文献

{"title":"Representation and normality of hyponormal operators in the closure of (mathcal{AN})-operators","authors":"G. Ramesh,&nbsp;S. S. Sequeira","doi":"10.1007/s10474-024-01493-0","DOIUrl":"10.1007/s10474-024-01493-0","url":null,"abstract":"<div><p>A bounded linear operator <span>(T)</span> on a Hilbert space <span>(H)</span> is said to be absolutely norm attaining <span>((T in mathcal{AN}(H)))</span> if the restriction of <span>(T)</span> to any non-zero closed subspace attains its norm and absolutely minimum attaining <span>((T in mathcal{AM}(H)))</span> if every restriction to a non-zero closed subspace attains its minimum modulus.</p><p>In this article, we characterize normal operators in <span>(overline{mathcal{AN}(H)})</span>, the operator norm closure of <span>(mathcal{AN}(H))</span>, in terms of the essential spectrum. Later, we study representations of quasinormal and hyponormal operators in <span>(overline{mathcal{AN}(H)})</span>. Explicitly, we prove that any hyponormal operator in <span>(overline{mathcal{AN}(H)})</span> is a direct sum of a normal <span>(mathcal{AN})</span>-operator and a <span>(2times2)</span> upper triangular <span>(mathcal{AM})</span>-operator matrix. Finally, we deduce some sufficient conditions implying the normality of them.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"341 - 359"},"PeriodicalIF":0.6,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On class operators for the lower radical class and semisimple closure constructions","authors":"N. R. McConnell,&nbsp;R. G. McDougall,&nbsp;T. Stokes,&nbsp;L. K. Thornton","doi":"10.1007/s10474-024-01492-1","DOIUrl":"10.1007/s10474-024-01492-1","url":null,"abstract":"<div><p>We construct the lower radical class and the semisimple closure\u0000for a given class using class operators and detail some of the properties of these\u0000operators and their interplay with the operators already used in radical theory.\u0000The setting is the class of algebras introduced by Puczy lowski which ensures the\u0000results hold in groups, multi-operator groups such as rings, as well as loops and\u0000hoops.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"275 - 288"},"PeriodicalIF":0.6,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On an application of the lattice of (sigma)-permutable subgroups of a finite group","authors":"A. -M. Liu,&nbsp;V. G. Safonov,&nbsp;A. N. Skiba,&nbsp;S. Wang","doi":"10.1007/s10474-024-01476-1","DOIUrl":"10.1007/s10474-024-01476-1","url":null,"abstract":"<div><p>Let <span>(sigma ={sigma_{i} mid iin I})</span> be some partition of the set of all primes and <span>(G)</span> a finite group. Then <span>(G)</span> is said to be <span>(sigma)</span>-full if <span>(G)</span> has a Hall <span>(sigma _{i})</span>-subgroup for all <span>(i)</span>; <span>(sigma)</span>-primary if <span>(G)</span> is a <span>(sigma _{i})</span>-group for some <span>(i)</span>; <span>(sigma)</span>-soluble if every chief factor of <span>(G)</span> is <span>(sigma)</span>-primary; <span>(sigma)</span>-nilpotent if <span>(G)</span> is the direct product of <span>(sigma)</span>-primary groups; <span>(G^{mathfrak{N}_{sigma}})</span> denotes the <span>(sigma)</span>-nilpotent residual of <span>(G)</span>, that is, the intersection of all normal subgroups <span>(N)</span> of <span>(G)</span> with <span>(sigma)</span>-nilpotent quotient <span>(G/N)</span>.</p><p>A subgroup <span>(A)</span> of <span>(G)</span> is said to be: <span>(sigma)</span>-permutable in <span>(G)</span> provided <span>(G)</span> is <span>(sigma)</span>-full and <span>(A)</span> permutes with all Hall <span>(sigma _{i})</span>-subgroups <span>(H)</span> of <span>(G)</span> (that is, <span>(AH=HA)</span>) for all <span>(i)</span>; <span>(sigma)</span>-subnormal in <span>(G)</span> if there is a subgroup chain <span>(A=A_{0} leq A_{1} leq cdots leq A_{n}=G)</span> such that either <span>(A_{i-1} trianglelefteq A_{i})</span> or <span>(A_{i}/(A_{i-1})_{A_{i}})</span> is <span>(sigma)</span>-primary for all <span>(i=1, ldots , n)</span>.</p><p>Let <span>(A_{sigma G})</span> be the subgroup of <span>(A)</span> generated by all <span>(sigma)</span>-permutable subgroups of <span>(G)</span> contained in <span>(A)</span> and <span>(A^{sigma G})</span> be the intersection of all <span>(sigma)</span>-permutable subgroups of <span>(G)</span> containing <span>(A)</span>.</p><p>We prove that if <span>(G)</span> is a finite <span>(sigma)</span>-soluble group, then the <span>(sigma)</span>-permutability is a transitive relation in <span>(G)</span> if and only if <span>(G^{mathfrak{N}_{sigma}})</span> avoids the pair <span>((A^{sigma G}, A_{sigma G}))</span>, that is, <span>(G^{mathfrak{N}_{sigma}}cap A^{sigma G}= G^{mathfrak{N}_{sigma}}cap A_{sigma G})</span> for every <span>(sigma)</span>-subnormal subgroup <span>(A)</span> of <span>(G)</span>.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"482 - 497"},"PeriodicalIF":0.6,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the second irreducibility theorem of I. Schur","authors":"A. Jakhar,&nbsp;R. Kalwaniya","doi":"10.1007/s10474-024-01478-z","DOIUrl":"10.1007/s10474-024-01478-z","url":null,"abstract":"<div><p>Let <span>(n)</span> be a positive integer different from <span>(8)</span> and <span>(n+1 neq 2^u)</span> for any integer <span>(ugeq 2)</span>. Let <span>(phi(x))</span> belonging to <span>(Z[x])</span> be a monic polynomial which is irreducible modulo all primes less than or equal to <span>(n+1)</span>. Let <span>(a_j(x))</span> with <span>(0leq jleq n-1)</span> belonging to <span>(Z[x])</span> be polynomials having degree less than <span>(degphi(x))</span>. Assume that the content of <span>(a_na_0(x))</span> is not divisible by any prime less than or equal to <span>(n+1)</span>. We prove that the polynomial \u0000</p><div><div><span>$$\u0000f(x) = a_nfrac{phi(x)^n}{(n+1)!}+ sum _{j=0}^{n-1}a_j(x)frac{phi(x)^{j}}{(j+1)!}\u0000$$</span></div></div><p>\u0000is irreducible over the field <span>(Q)</span> of rational numbers. This generalises a well-known result of Schur which states that the polynomial <span>( sum _{j=0}^{n}a_jfrac{x^{j}}{(j+1)!})</span> with <span>(a_j in Z)</span> and <span>(|a_0| = |a_n| = 1)</span> is irreducible over <span>(Q)</span>. For proving our results, we use the notion of <span>(phi)</span>-Newton polygons and a few results on primes from number theory. We illustrate our result through examples.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"289 - 298"},"PeriodicalIF":0.6,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geodesic loops on tetrahedra in spaces of constant sectional curvature","authors":"A. Borisenko,&nbsp;V. Miquel","doi":"10.1007/s10474-024-01475-2","DOIUrl":"10.1007/s10474-024-01475-2","url":null,"abstract":"<div><p>Geodesic loops on tetrahedra were studied only for the Euclidean space and it was known that there are no simple geodesic loops on regular tetrahedra. Here we prove that: 1) In the spherical space, there are no simple geodesic loops on tetrahedra with internal angles <span>(pi/3 &lt; a_i&lt;pi/2)</span>or regular tetrahedra with <span>(a_i=pi/2)</span>, and there are three simple geodesic loops for each vertex of a tetrahedra with <span>(a_i &gt; pi/2)</span>and the lengths of the edges <span>(a_i&gt;pi/2)</span>. 2) We obtain also a new theorem on simple closed geodesics: If the angles <span>(a_i)</span>of the faces of a tetraedron satisfy <span>(pi/3 &lt; a_i&lt;pi/2)</span>and all faces of the tetrahedron are congruent, then there exist at least <span>(3)</span> simple closed geodesics.\u00003) In the hyperbolic space, for every regular tetrahedron <span>(T)</span>and every pair of coprime numbers <span>((p,q))</span>, there is one simple geodesic loop of type <span>((p,q))</span> through every vertex of <span>(T)</span>.\u0000The geodesic loops that we have found on the tetrahedra in the hyperbolic space are also quasi-geodesics.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"360 - 375"},"PeriodicalIF":0.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01475-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some properties of the ideal of nowhere dense sets in the common division topology","authors":"M. Kwela","doi":"10.1007/s10474-024-01481-4","DOIUrl":"10.1007/s10474-024-01481-4","url":null,"abstract":"<div><p>We consider the ideal of nowhere dense sets in the common division topology (Szyszkowska’s ideal), and examine some of its basic properties. We also explore the possible inclusions between the studied ideal and Furstenberg’s and Rizza’s ideals, thus answering open questions posed in a recent article by A. Nowik and P. Szyszkowska [17]. Moreover, we discuss the relationships of the Szyszkowska’s ideal with selected well-known ideals playing an important role in number theory and combinatorics.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"299 - 311"},"PeriodicalIF":0.6,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01481-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Concurrent normals problem for convex polytopes and Euclidean distance degree","authors":"I. Nasonov,&nbsp;G. Panina,&nbsp;D. Siersma","doi":"10.1007/s10474-024-01483-2","DOIUrl":"10.1007/s10474-024-01483-2","url":null,"abstract":"<div><p>It is conjectured since long that for any convex body <span>(Psubset mathbb{R}^n)</span> there exists a point in its interior which belongs to at least <span>(2n)</span> normals from different points on the boundary of <i>P</i>. The conjecture is known to be true for <span>(n=2,3,4)</span>.</p><p>We treat the same problem for convex polytopes in <span>(mathbb{R}^3)</span>. It turns out that the PL concurrent normals problem differs a lot from the smooth one. One almost immediately proves that a convex polytope in <span>(mathbb{R}^3)</span> has 8 normals to its boundary emanating from some point in its interior. Moreover, we conjecture that each simple polytope in <span>(mathbb{R}^3)</span> has a point in its interior with 10 normals to the boundary. We confirm the conjecture for all tetrahedra and triangular prisms and give a sufficient condition for a simple polytope to have a point with 10 normals. \u0000Other related topics (average number of normals, minimal number of normals from an interior point, other dimensions) are discussed.\u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"522 - 538"},"PeriodicalIF":0.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some special Z-symmetric manifolds with applications to space-times and Ricci solitons","authors":"B. Kirik Rácz,&nbsp;B. Cindik","doi":"10.1007/s10474-024-01480-5","DOIUrl":"10.1007/s10474-024-01480-5","url":null,"abstract":"<div><p>This work aims to investigate various properties of some special <i>Z</i>-symmetric manifolds and their applications on space-times. Having an important place of the study, classifications of second-order symmetric tensor fields on space-times and holonomy theory are considered. <i>Z</i>-symmetric manifolds in the holonomy structure are investigated and some results are obtained. Various special vector fields are examined on <i>Z</i>-recurrent and weakly <i>Z</i>-symmetric manifolds and some relations associated with the eigenvector structure of the <i>Z</i>-tensor are found. In addition, several examples related to the outcomes of the study are given. Finally, some links between the <i>Z</i>-tensor and Ricci solitons on space-times are determined. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"408 - 428"},"PeriodicalIF":0.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete reflexivity in topological groups and function spaces","authors":"V. V. Tkachuk","doi":"10.1007/s10474-024-01479-y","DOIUrl":"10.1007/s10474-024-01479-y","url":null,"abstract":"<div><p>We show that pseudocharacter turns out to be discretely reflexive\u0000in Lindelöf <span>(Sigma)</span>-groups but countable tightness is not\u0000discretely reflexive in hereditarily Lindelöf spaces. We also\u0000establish that it is independent of ZFC whether countable\u0000character, countable weight or countable network weight is\u0000discretely reflexive in spaces <span>(C_p(X))</span>. Furthermore, we prove\u0000that any hereditary topological property is discretely reflexive\u0000in spaces <span>(C_p(X))</span> with the Lindelöf <span>(Sigma)</span>-property. If\u0000<span>(C_p(X))</span> is a Lindelöf <span>(Sigma)</span>-space and <span>(L D)</span> is a\u0000<span>(k)</span>-space for any discrete subspace <span>( { D C_p(X) } )</span>, then it is\u0000consistent with ZFC that <span>(C_p(X))</span> has the Fréchet–Urysohn\u0000property. Our results solve two published open questions. \u0000</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"498 - 509"},"PeriodicalIF":0.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convolution operators and variable Hardy spaces on the Heisenberg group","authors":"P. Rocha","doi":"10.1007/s10474-024-01484-1","DOIUrl":"10.1007/s10474-024-01484-1","url":null,"abstract":"<div><p>Let <span>(mathbb{H}^{n})</span> be the Heisenberg group. For <span>(0 leq alpha &lt; Q=2n+2)</span> and <span>(N in mathbb{N})</span> we consider exponent functions <span>(p (cdot) colon mathbb{H}^{n} to (0, +infty))</span>, which satisfy log-Hölder conditions, such that <span>(frac{Q}{Q+N} &lt; p_{-} leq p (cdot) leq p_{+} &lt; frac{Q}{alpha})</span>. In this article we prove the <span>(H^{p (cdot)}(mathbb{H}^{n}) to L^{q (cdot)}(mathbb{H}^{n}))</span> and <span>(H^{p (cdot)}(mathbb{H}^{n}) to H^{q (cdot)}(mathbb{H}^{n}))</span> boundedness of convolution operators with kernels of type <span>((alpha, N))</span> on <span>(mathbb{H}^{n})</span>, where <span>(frac{1}{q (cdot)} = frac{1}{p (cdot)} - frac{alpha}{Q})</span>. In particular, the Riesz potential on <span>(mathbb{H}^{n})</span> satisfies such estimates.</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 2","pages":"429 - 452"},"PeriodicalIF":0.6,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}